"They called me straightaway," recalls the 75-year-old Alexandre, as he sits in a bar off the Champs-Elysees. "I jumped in a plane and went to London. There, in her hospital bed, she was held up by three nurses while I created her famous artichoke cut." (This is the spiky style she still sports today.)
This year marks his 60th anniversary in the profession, and over the years, Taylor has been only one of a quite staggering star-studded cast of clients. Most famously, he was the Duchess of Windsor's hairdresser for 30 years. He was also Princess Grace's for 26. Sophia Loren has had more than 500 appointments with him. Greta Garbo was not only a client, but also "a friend". Jean Cocteau popped by regularly to have his hair permed. He did Maria Callas's hair both on and off stage and has styled the locks of almost every female royal in Europe, including Princess Margaret, Princess Anne and the Duchess of Kent.
He has also been the haute couture hair-stylist par excellence. For 34 years, he created the looks for Saint Laurent's shows. He also worked with Givenchy for 25 years. with Coco Chanel for 20 and at one time or another for Dior, Ungaro, Lacroix and Karl Lagerfeld. Even today he is still very much in demand. When Jean-Paul Gaultier decided to present his first haute couture collection last year, he immediately gave Alexandre a call.
"He is Alexandre the Great," declares Gaultier. "He is still very on the ball, not at all blase, and incredibly modest."
Thierry Mugler adds: "He is one of the living legends of our profession. He is charming, a great professional, and is still ready to call into question what he does, which is remarkable after so many years."
Mugler is the only designer for whom Alexandre continues to work personally, although the salon which bears his name also collaborated on the haute couture shows in July of Jean-Louis Scherrer, Louis Feraud and Valentin Yudashkin.
Alexandre admits: "I have a little weak spot for Monsieur Mugler. But for the other designers, I just take my seat in the audience and watch the work of my pupils."
Indeed, he officially retired six years ago and handed over the reins of the Alexandre de Paris salon to its present artistic director, Jean- Luc Minetti. However, he is still omnipresent. He is consulted about styles for the shows, and important weddings. He also lives above the salon on Avenue Matignon, and pops in daily.
As you open the door to the building, a quite overwhelming stench of hair lacquer almost strikes you down. There are several VIP rooms, one of which bears the name Sphinx. It is there that Alexandre receives his two remaining personal clients - the actress Sophia Loren and the Countess of Paris.
When I arrive, Alexandre himself is in the reception area, gossiping animatedly with a couple of wet-haired clients. He wears a dogstooth jacket and a stripy red shirt with a bow. Glasses hang on a gold chain around his neck. He remains spritely and there is more than a hint of high camp about the way he speaks.
He was born in 1922 in Saint Tropez, the son of a couple of restaurant owners. They wanted him to become an army doctor. However, from an early age he wanted to work in fashion. A key influence came in the form of the wife of the painter Dunoyer de Segonzac, whose avant-garde, closely cropped haircut fascinated him. She informed him that she went to "the emperor of hairdressers", Antoine, in Cannes. Antoine had started his career by doing the great actress Sarah Bernhardt's hair, had created the short garcon look with Chanel in 1925 and had also given Josephine Baker her gelled-down, kiss-curled cut.
In 1938, Alexandre started training with Antoine, and was soon tending the tresses of royalty. In 1946, he did the hair of the Begum Aga Khan for a ball she gave to celebrate her marriage. Among the guests was the Duchess of Windsor.
"The very next day, she called me and asked me to go and see her," recounts Alexandre. "She gave me a thousand explanations as to what she wanted, and then I did her hair. The next day I got another call.
"`What did you do to my hair?' she asked. "`I disobeyed you and did exactly the opposite of what you requested,' I admitted.
"`It's wonderful! For the first time in my life, I woke up with my hair exactly as it was when I went to sleep. From now on, you will stay by my side.'" The duchess was true to her word and kept her promise. And so Alexandre had found his "wife of a king".
"They were like parents to me," he says with a hint of nostalgia. They persuaded magazines to write profiles of him. The Duke gave him lessons in how to dress. The Duchess introduced him to 400 clients, and taught him how to arrange flowers and to set the table. In return, Alexandre would do her hair every evening.
It was "Mademoiselle" Chanel who introduced him to Jean Cocteau, who designed his logo. His rendezvous with Greta Garbo were always quite secretive.
"When she came to the salon, she would say: `Hide me! Don't let anyone see me,'" he says. "She also told me: `I hate hairdressers. Don't style my hair. Cut it!'" So he simply gave her a fringed bob.
When Jackie Kennedy came to France he scattered diamonds in her hair. Before he could touch the locks of the King of Thailand, he had to have his hands blessed.
As time went on, Alexandre became almost as famous as his clients. He was invited to all of Marie-Helene de Rothschild's balls, as well as the famed Bestegui ball in Venice. The Italian film director Vittorio de Sica asked him to play himself alongside Shirley MacLaine in Woman Times Seven, and Liz Taylor insisted that Franco Zeffirelli create a role for him in the film version of The Taming of the Shrew.
Asked why women appreciated him so much, he replies: "I never revealed any secret I heard. They had confidence in me and knew that I would not repeat anything."
Even now he is retired, celebrities such as Jodie Foster, Victoria Abril and Sophie Marceau continue to flock to the salon that bears his name. Plans are afoot to open an Alexandre de Paris in Moscow next year; the management is also looking for a location in London.
Alexandre himself is also looking ahead - to an exhibition about his career which he is planning for Paris next year. Looking back, he certainly seems to have no regrets.
"Is there anyone else you would have loved to have had as a client?" I ask. "No," comes the immediate reply. "I have done the hair of all the women I dreamed of."