Similarly smitten was one Robert Zimmerman. On the cover of his 1964 album, Another Side Of Bob Dylan, he had even name-checked Hardy in a poem. In summer 1966, moreover, Dylan was on his way to Paris to make his French debut at the Olympia theatre. Hardy, very much a Dylan fan, was well aware of this, but feared her filming commitments in Monte Carlo might prevent her from attending.
"Right up until the last moment, I didn't know if John Frankenheimer would let me go," she says. "Finally I got authorisation, but unfortunately the concert was poor. During the intermission someone came to tell me that Dylan wouldn't come back onstage unless I went to see him in his dressing room. It was surreal, but I went. He looked very thin and sickly, which may explain why the concert was so bad.
"Later, a crowd of us went to the George V Hotel, and Bob played me `I Want You' and `Just Like A Woman' on his guitar in his room. They were new songs then - can you imagine the thrill? When he came to Paris not so long ago, he still asked for me - or at least that's what I read in the newspapers. I am too afraid to go and say hello now. He probably remembers me as I was."
Despite her misgivings, one imagines Dylan would still find Hardy an attractive sight. Even dressed-down in a black V-neck sweater and black jeans teamed with pink ballet slippers, she's a trim and strikingly elegant- looking 61-year-old with a vivacious, easy smile.
We're chatting in the minimalist, Zen-like surrounds of her 7th arrondissement apartment. Just four minutes walk from the Arc de Triomphe, it's a home she shares with the musician and actor Jacques Dutronc. Dutronc, as famous as Hardy in France, has been her partner for 37 years, and her husband for 23 years. "When we married in 1981 for fiscal reasons, our son Thomas was already seven," she laughs. "If it wasn't for the inheritance laws, no one in France would marry."
Hardy says she occupies the windowless ground floor of the flat, while her husband enjoys free reign upstairs. A well-stocked bar - Dutronc's presumably - is visible through a portion of glass ceiling above us. In the luxurious, marble-tiled room in which we are sitting, a glass-fronted wine chiller purrs softly, as though pleased with the expensive-looking stash of whites within.
Ostensibly, we've met to talk about Tant De Belles Choses (So Many Beautiful Things), Hardy's first album of all-new material in eight years. Naturally we do so, but the normally reclusive star also speaks about her adventures with the beau monde in 1960s London, her passion for astrology, and much more besides.
Having playfully mocked my attempt to greet her in French, she shows our translator, Jane, and me to a low coffee table dominated at one end by a huge statue of Buddha. "My husband is very fond of it," says our host, "but I am the one with an interest in Buddhism."
Hardy signed to Vogue Records at 17. The composer Francis Poulenc was among those who offered her songs but, like much of her later work, Hardy's debut single was her own composition. "Tous les garcons et les filles" eventually sold more than two million copies, charting in the UK and the rest of Europe. The French press noted that Hardy had sold more records in 18 months than Edith Piaf did in 18 years.
Fortuitously, her rise coincided with the emergence of a uniquely Gallic genre of pop music known as Ye-Ye. But while other Ye-Ye girls such as Sylvie Vartan and Brigitte Bardot largely dealt in frivolity, Hardy's music had a thoughtful, often melancholic quality that set her apart. "Ophelia without the delirium," wrote one critic, capturing something of her early work's flavour. But Hardy, unlike Shakespeare's Ophelia, was no victim.
She says that she was an "incredibly naive" teenager. Naivety is not to be confused with stupidity, however, and the 18-year-old Francoise had already studied political science, then literature at the Sorbonne. "I was always more interested in nourishing my mind than worrying about how I looked," she explains. Reading between the lines, one imagines Hardy was one of those ingenues, who, initially at least, was unaware of the devastating power of her beauty. Unsurprisingly, this made her all the more alluring to the renowned photographer Jean-Michelle Perier.
Together with designers such as Courreges and the aforementioned Paco Rabanne, Perier, something of a Pygmalion figure, is credited with transforming Hardy into the sophisticated it-girl so many British rock stars found irresistible. The pair met while Perier was photographing Hardy for Salut les Copains magazine, and quickly became lovers.
Soon, she was the first singer of her generation to grace the cover of Paris Match, and by 1965, she was singing at London's Savoy Hotel in support of her album Ce Petit Coeur. Famously, and to the delight of a Savoy crowd that included The Rolling Stones, she wore a metal, Rabanne-designed dress that, despite its brevity, weighed 16 kilos. Does she by any chance still have it? "No, I finally threw it out a few years ago," she says, without a trace of nostalgia. "You can't keep everything."
And what of Mick Jagger? They were photographed together and he was obviously attracted to her. Might they have become lovers had circumstances been different?
"Who can say?" she says, smiling. "We did go out for dinner, but we both had partners at the time. Plus our mutual attraction may have been superficial. It's very easy to be attracted from afar by someone who is good-looking, talented and famous. I think I was too clean for Mick Jagger, though. I didn't know anything about drugs, for example, and wouldn't have been tempted by them.
"I remember Brian Jones and his girlfriend Anita Pallenberg invited me to their home. Like any young girl at the time I was thrilled, because he was one of The Rolling Stones. Not the one I was most interested in, but a Stone none the less. They wondered whether I had accepted their invitation because I was interested in him or interested in her." She laughs. "My boyfriend Jean-Michelle Perier would be away on assignments, and some people assumed I was a lesbian.
"But I never felt that English men were trying to hit on me in any case. The only one who ever did was the late David Hemmings [Hemmings played the photographer Thomas in Michelangelo Antonioni's 1966 film Blow-Up], and he wasn't my type. I did have a brief love-affair with another young British actor, but I can't tell you his name..."
Hardy's childhood has sometimes been described as troubled. Her unmarried mother, Madeleine, was an assistant accountant who raised Francoise and her younger sister Michele alone in Paris's 9th arrondissement. The singer has described her strict maternal grandmother as "neurotic and over-bearing," and by all f accounts her absentee father contributed little to her upbringing, save for the Spanish guitar upon which she first began writing songs while at boarding school in Austria.
She says that this background bred self-dependence, shyness, and an ongoing love of solitude. "What I love since we moved to this apartment," she adds by way of illustration, "is walking in the Bois de Bologne. For me, being in the woods alone is a form of meditation that brings me closer to the Divine than a church ever could."
So hell, as Jean-Paul Sartre had it, really is other people?
"No, I think that's too loose an idea. You can flip it like a pancake and say `hell is myself'."
With Hardy's independence, some claimed, came an aloof manner. Indeed, the strained atmosphere during the recording of her 1977 album, Star, with arranger Gabriel Yared led some to refer to her as an "ice queen". Today she seems mindful of her privacy, maybe a little dry at times, but certainly not cold.
"What is this word `aloof'?" she asks. When our translator explains, Hardy responds: "sometimes I might seem aloof if I feel uneasy, but in a situation such as this where you are on my territory, I'm perfectly at ease. When Radiohead played Paris I was so impressed with Thom Yorke that I didn't feel able to talk with him much, so maybe he thought me cold. The problem is that he is shy, too. I spent most of the evening chatting with the guitarist Ed [O'Brien]. He's very easy to be with."
We talk more about how shyness is sometimes misconstrued as coldness, then I ask Hardy why her film career ended with 1967's Grand Prix. She says she never enjoyed being in front of the camera, and always had problems with the way directors presented her. "Memory is a very disappointing thing," she adds, when quizzed about her brief appearance in the 1965 comedy, What's New, Pussycat?, scripted by Woody Allen. "I remember nothing of the filming; only that I accepted the part in the hope of catching a glimpse of Peter O'Toole. I thought, `I'm going to work with him, and get paid also? That can't be bad!'"
Clearly, the young Hardy was often star-struck. And even at the start of 1995 when Brit poppers Blur began singing her praises and Hardy was approaching 51, she didn't dream of contacting them about a collaboration, much as the idea appealed. But then she saw Damon Albarn being interviewed on MTV ("He had something special about him which reminded me of my husband"), and two days later she was amazed to receive a fax from the band's record company saying that their dearest hope for the New Year was to record with her.
"Two days after that, they were in my house," she laughs. "I thought Damon was a very tender, delicate person. I wondered why they wanted to record `To The End' with me, but I found out that Graham (Coxon; ex-Blur guitarist) was very fond of some of my past work. Later, I heard that the others wanted to work with me to please Graham, but I don't know if that's true."
On Hardy's new album, Tant De Belles Choses, the songs are starkly melancholic or sweetly heart-warming by turns. The thread that binds is her classy, assured vocal delivery, set against in some songs, trip-hop arrangements, in others, a traditional, acoustic-jazz backdrop. Her husband and son, both accomplished guitarists, lend a hand, as do the Irish songwriter Perry Blake, and the English songwriter Ben Christophers. All told, it's a sophisticated, affecting work by a woman whose creative powers are undiminished.
One of the album's key themes is the tragedy of amour, and with the title track documenting a dying woman's farewell to her lover, it's not always an easy listen. The stand-out track "Sur Quel Volcan?" ("On Which Volcano?") partly concerns "reaching our limits in terms of polluting the planet", but also alludes to "a hidden love affair that would be destructive if people were to find out about it". Only on the Eurostar home does it occur to me that I should have asked Hardy if the song is about her own tryst with the mysterious "young British actor" she mentioned earlier.
Aside from music, Hardy's other great passion is astrology. In 1974, having met astrologer Jean-Pierre Nicola and been fascinated with his advances in the field, she began taking private classes with him. She eventually became a specialist on astrological birth charts, and started pursuing astrology in a semi-professional capacity. In 1986, she and graphologist Anne-Marie Simond published Between The Lines, Between The Signs, a book analysing the handwriting and star signs of Gallic celebrities such as Serge Gainsbourg and Jane Birkin. Between 1980 and 1982, moreover, Hardy and actor Benoit Allemane co-presented an astrology-themed talk show on Radio Monte Carlo.
Pragmatic, ambitious, a little reserved, Hardy seems to display some of the purported traits of a typical Capricorn. But how does astrology impact upon her everyday life?
"It's a source of intellectual stimulation for me," she says. "People ask if I make decisions based on my horoscope, and the answer is no, never. If something important or challenging is happening in my life, I will use astrology to help me make sense of it, but I don't rely on astrology alone."
By now our interview time is up, so I close by asking the former literature student what she reads now. "Edith Wharton, Colette, Henry James ...," she says, before draining the last of her glass of Perrier. "So many contemporary books don't deserve to be read, but the classics you can come back to again and again."
As she shows us to the door, all posture and poise, it strikes me that Hardy is something of a classic, too. Charming, enigmatic, iconic and enduring, she is possessed of a life-story people will be reading about for decades to come. E
`Tant De Belles Choses' is out on EMI Liberty