He acts with just one eye throughout, but you won’t see a more remarkable performance all year than Mathieu Amalric’s in The Diving Bell and the Butterfly. He plays Jean-Dominique Bauby, a former editor of French Elle, who was suddenly paralysed with “locked-in syndrome”, a rare condition in which the brain stem is incapacitated, leaving him unable to move anything but his left eyelid. For an actor used to manipulating his body for meaning, this was Hell on Earth. “It’s very, very hard not to move,” Amalric explains, when we meet on a hotel terrace on the French Riviera. “Try it for two hours! Just try it. You have to move your muscles not to move. You’re always contracted, so it’s exhausting. At the end of each day I couldn’t do anything. It’s as if I’d done an action film!”

The closest the 41-year-old Amalric has come to that was in his most internationally noteworthy role to date, as the mysterious mercenary Louis, who plays the Israelis off against the Palestinians in Steven Spielberg’s terrorism story Munich.

It was Spielberg’s long-term producer Kathleen Kennedy who gave him the script for The Diving Bell and suggested to the director, Julian Schnabel, that Amalric was worth considering for the role. As Amalric points out, The Diving Bell was an incredibly personal project for Schnabel, who won Best Director for it in Cannes. “He lost his father,” Amalric explains. “He saw his father, who was afraid to die, and he felt that he couldn’t help him. That was awful for Julian.”

Schnabel is also friends with Javier Bardem, who played a similarly paralysed quadriplegic in Alejandro Amenebar’s The Sea Inside.

Amalric sees the two films as wildly different. “ The Sea Inside is the story of a man who struggles to die. He wants to die. The struggle of Bauby is something to do with life. He didn’t think he was going to die. He died of something very stupid, an infection. He wanted to live.”

Bauby died in 1997, just days after the publication of his memoir on which the film is based. Written using a crude system of blinking to communicate, his remarkable account drives the film. It helped Amalric to find the man’s voice, particularly useful given that the first half is shot entirely from Bauby’s perspective, accompanied by a wry interior monologue that conveys both the horror of his situation and the humour with which he dealt with it. I ask whether playing Bauby had changed Amalric’s perspective on death. “No, it changed more something about my life,” he snaps back. “Sometimes I think of Bauby and take 30 seconds to remember that life is absolutely marvellous.”

Amalric, one of the most respected actors in France, has an oddly squashed face that defiantly resists any attempt to cast him as a conventional leading man. He was born in the wealthy Parisian district of Neuilly-sur-Seine, the son of two Le Monde journalists, and gravitated towards the film industry. He began as a trainee assistant director on Louis Malle’s 1987 classic Au Revoir, les Enfants when he was barely out of his teens. He spent the next decade working on film sets with a view to becoming a film-maker himself. This he eventually realised, making three modest feature films, including the 2001 comedy Le Stade de Wimbledon, in which he directed his former wife, Jeanne Balibar.

But by this point he had found a lucrative secondary career, which “came completely by accident” when the director Arnaud Desplechin convinced him to take a small role in his 1992 thriller The Sentinel. But it’s clear that he’s uncomfortable with his on-screen success. Despite going on to make more than 50 films in the past 15 years, including André Téchiné’s Alice et Martinopposite Juliette Binoche, and recently The Singer with Gérard Depardieu, he still doesn't consider himself an actor. “It’s a game,” he says. “Each time, I’m saying to myself, ‘People will see that I’m not an actor and it will stop’.” He looks horrified when I suggest that the success of Munichmay have offered him a Hollywood career. “I don’t want to be a star!” he cries.

Now he seems to be challenging Depardieu as the hardest-working actor in France. But he has vowed not to act for the next 18 months as he prepares to direct his own love story set in the world of burlesque. He even turned down the chance to star in William Friedkin’s forthcoming Coco & Igor, the story of Coco Chanel’s relationship with Igor Stravinsky. “Now I have the strength to continue my stuff,” he says. Bauby would be proud.

The Diving Bell and the Butterfly is at The Times BFI London Film Festival, Sun, at OWE2 at 8.30pm; Mon, OWE1, 3.30pm

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