Paris, 1913. Igor Stravinsky’s The Rite of`Spring has its premiere in front of the well-heeled denizens of the Champs Elysées theatre. Nijinsky has choreographed an accompanying ballet which matches the daring, avant-garde spirit of the music. But it's too radical for the conservative audience. Soon the music is drowned out by the jeers and boos of the outraged punters. Fistfights break out between rival factions in the stalls. The gendarmes attempt to restore order and Nijinsky shouts and claps to keep time for the dancers who can no longer hear the orchestra over the cacophony. It’s a scandal. Watching in the audience was Coco Chanel.

The meticulous re-creation of the riotous debut of The Rite of Spring is one of the main strengths of Jan Kounen’s handsome but rather stodgy drama about the romance between the composer and the designer. His film, which closed the Cannes Festival, is hugely ambitious and gloriously chaotic. But although the cartoonish, often crass ultra-violence of Kounen's earlier films, particularly Dobermann and Blueberry, stirred their own heated controversies on release, his latest faces no such fate. It is an uncharacteristically conventional piece of film-making for a former enfant terrible.

Anna Mouglalis brings exactly the right kind of calculating froideur to the role of Coco Chanel, not to mention an effortless chic and the clothes hanger frame that made the designer the style icon she was. The exquisite costumes – which will be reason enough for fashion fans to watch the film – flow around her lean, angular form like liquid. The Danish actor Mads Mikkelsen is rather less compelling as Stravinsky. He has mastered the technical aspects of the role – his Russian sounds persuasive enough to an untutored ear and his fake piano playing is suitably frenzied. But he lacks the intensity. Rather than brooding passion, Mikkelsen’s demeanour conveys a kind of sullen irritation. And while individually they are both undeniably interesting subjects for film treatment, I’m not convinced that their affair exerts the fascination that the film-makers hoped it would.

Kounen juxtaposes scenes of tortured creativity from both artists: Stravinsky bashes away at the keyboard, Chanel wrangles a particularly challenging sequin problem. But the scenes when they are together on screen simply fail to ignite. It’s a great pity because, in terms of the design at least, the film is a thing of real beauty. Coco’s monochromatic wardrobe is echoed everywhere – from the black and white of the piano keys to the gorgeous art nouveau-inspired interiors of her country retreat. Unfortunately, even in the world of haute couture, looks aren’t everything.

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