Michael Schumacher had intended to spend his 45th birthday surrounded by friends in his chalet in the ski resort of Méribel. His management had earmarked the date to relaunch his website, showcasing the record-breaking Formula One champion's life after retiring from competitive sport. But instead, Schumacher wason Friday lying in a critical but stable condition in a clinic at the foot of the French Alps, as fans gathered outside the hospital to mark his birthday.

He has been in an induced coma since suffering a severe brain trauma in a skiing accident just after 11am on Sunday, only about 500 metres from his high-security chalet. He was airlifted to a hospital in Moûtiers then to a specialist clinic in Grenoble, where doctors stabilised his condition by reducing the swelling of his brain.

On Friday, Schumacher's wife Corinna, brother Ralf, father Rolf, son Mick and daughter Gina-Maria have spent much of the past few days and nights at his bedside.

Over the course of Friday, buses with about 500 Italian Ferrari fans pulled up in the driving rain. Mostly clad in red-and-white and carrying flags and banners, they said they had gathered to show their "silent support". Schumacher won five of his seven Formula One titles for the car manufacturer based in Maranello. "Schumi, all our thoughts for you and your family," read one of the banners. "Sempre Schumi", said another. Some fans were carrying letters addressed to him. In the evening, a light projection spelled out a message of support on the clinic's facade: "45. Schumi: Stay Strong, Keep Fighting".

Over the course of the week, fans from around the world have expressed support. China's state press agency, Xinhua, wished him "gute Besserung", or a speedy recovery, in German. In London, the footballer Jack Wilshere tweeted a picture from Arsenal's dressing room of the team holding a sign saying "Get well Schumi".

A supporter holds a greeting card for Michael Schumacher at the hospital in Grenoble where he is being treated. Photograph: David Ebener/dpa/Corbis

On Thursday, Schumacher's family released a message via his website, expressing gratitude for the support. "We all know that Michael is a fighter and won't give up," it said. "Thank you."

Sabine Kehm, Schumacher's manager, a former sports journalist who has worked with the driver for the past 14 years, denied reports that he had been skiing at "high speed" and said he had only ventured into the area between the two pistes Biche and Mauduit because he had stopped beforehand, to help one of his friend's daughters who had taken a tumble on the slopes.

After pushing himself off, Schumacher had hit a snow-covered rock and lost balance, hitting another rock head-first, his helmet splitting on impact. What at first had looked like deliberate risk-taking now increasingly looks more like an unfortunate accident.

French investigators said they would interview Kehm to establish the exact cause of the accident. Schumacher's son Mick, 14, who was with his father at the time of the accident, was interviewed on Friday, French newspaper L'Equipe reported.

On Friday night, French TV reported that Schumacher's family had handed over a camera, which was mounted on his helmet, to investigators.

Five years ago, on Schumacher's 40th birthday, the tabloid Bild ran a long interview in which other athletes asked the driver questions.

Responding to a question about his passion for motorbiking, Schumacher said: "If you are in control of something, you can also calculate the risk. And the remaining risk, which you can't calculate, you get that anywhere in life. That's fate. That's how I see it."