Left of centre: Celebrating 40 years of Sonia Rykiel

When someone can be recognised by their hair alone, it's a vivid sign that they have attained cult status. Karl Lagerfeld has his trademark ponytail and Anna Wintour her signature bob, but Parisian designer and Left Bank legend Sonia Rykiel outdoes them both with her crimped mane of bonfire red hair.

When I meet the designer at her bohemian St Germain apartment, it's immediately obvious why her incandescent tresses, set off by fine white skin and hauntingly high cheek bones, informed several designers' tributes at Rykiel's 40th anniversary show in October. For the climax of the event, organised by her daughter Nathalie, 30 models came out wearing Rykiel-inspired looks by renowned designers. Martin Margiela created a dress made of frizzy orange fur while a flame-haired model sported a jumper dress with giant knitting needles by Jean Paul Gaultier. "I was so surprised," Rykiel says. "I saw all these models dressed like me and I thought what is that? It was crazy. Such a fantastic surprise." The designer's career will also be marked by a major retrospective at the Musée des Arts Décoratifs in Paris. The exhibition will explore the Rykiel mythology through videos, clothes and photographs by the likes of Dominique Isserman and Sarah Moon.

Rykiel's hair is just one of many familiar motifs that she has made her own over the years; stripes, whorled corsages, glitter, quirky knitwear, slogans and pop images such as cherries and hearts all immediately evoke her off-beat aesthetic. She is often referred to as the "thinking woman's designer", but the daydreaming woman's designer might be just as apt a description. Hers isn't so much a rigorous, intellectual label as one with a sense of whimsy and humour that has characterised her work over and above an observance of trends. Women love her clothes because they are imaginative, sexy and fun – qualities that are reflected in the mood of the models on her catwalks. Rykiel is one of the few designers who actually encourages her models to look cheerful – "I say smile, look happy, pick a man in the audience and look at him like this," she says miming the most coquettish of expressions and tossing her hair in a manner that suddenly takes off about 60 of her well-maintained 78 years.

The eldest of five daughters in a Russian Jewish family, born just outside Paris, Rykiel's ambitions as a young woman were, she tells me, "to have 10 children, but because I only had two, I got bored and decided to work". She married a boutique owner in 1960, from whom she separated a few years later and began designing maternity clothes and fitted sweaters, one of which appeared on the cover of Elle magazine. In 1968 Women's Wear Daily dubbed her the Queen of Knits, and in May of the same year, in the midst of the student riots, she opened a shop on the rue de Grenelle. "I opened it in the morning and closed it in the evening," she says, "it was close to The Sorbonne and there were students demonstrating everywhere. Then I opened it again two months later." The atmosphere on the Left Bank was, "fun, mysterious, interesting, happy. There was something in the air. Paris was a melting pot, it felt like San Francisco had come to the Left Bank."

With her radical creations, Rykiel's boutique offered a fresh alternative to many of the more rigid designs of the time. "People seemed astonished by what I was doing, my shop was different because then everything was couture or the beginning of prêt-à-porter and there weren't many small boutiques." In the early 1970s the thoroughly modern Madame Rykiel pioneered clothes with exposed seams, and no hems or linings. Dominique Isserman has remarked on how unbelievably modern Rykiel's designs still look. "Surely that is because I was interested in the woman, rather than in fashion," the designer explains, with a dismissive Parisian wave of her hands.

Although Rykiel's shops still have the feel of one-off boutiques – albeit very glossy ones – and she remains one of the few designers to keep the business in the family; she now has 60 shops across the world, from Tokyo to Moscow. The brand also encompasses childrenswear, menswear, the Sonia by Sonia Rykiel diffusion label, and perfume. Rykiel has never been content to be only a fashion designer, and has published several books, including a novel called The Red Lips and a collection of fairy tales, and released a record with Malcolm McLaren in 1994. She has been a muse, providing the inspiration for one of the characters in Robert Altman's film Prêt-à-Porter, and posing for Andy Warhol. Amidst the sketches of Rykiel by Lacroix and her longtime friend Karl Lagerfeld, arranged around the open fireplace in her living room, is a large Warhol portrait of the designer. She is depicted in profile, her chin resting on her hand.

Being herself, and designing for herself – rather than second guessing trends – has given her collections the idiosyncratic character that has been the secret of Rykiel's success. She says, "comfortable means nothing, feminine means nothing, masculine means nothing. I want my designs to be objects of desire. I love the way you can see something and think, 'That is me!'." Which is just what happens with Sonia Rykiel's clothes.

Sonia Rykiel: Exhibition starts Thursday to 19 April 2009 at La Musée des Arts Décoratifs, 107 rue de Rivoli, Paris 75001 (00 33 1 44 55 57 50; lesartsdecoratifs.fr)