Formula One legend Michael Schumacher remained in critical condition on Sunday a week after his skiing accident in the French Alps, which a German witness said he inadvertently filmed on his smartphone.

Investigators are focusing on the retired racer’s speed when he fell and slammed his head on a rock on a small off-piste section of the Meribel ski resort, prompting his evacuation by helicopter to the Alpine city of Grenoble.

They are hoping that a helmet-mounted camera Schumacher was wearing will provide some clues, as will footage by a 35-year-old steward who says he was filming his girlfriend on the slopes when by chance he captured the moment when the driver fell.

In the background, a skier is seen descending an unmarked run between two groomed pistes before falling, news magazine Der Spiegel reported.

According to the witness, who spoke to the magazine, the seven-time world champion was descending the slope at a “leisurely” pace – “a maximum speed of 20 kilometres an hour”. He plans to hand over the footage to French investigators.

This would corroborate claims by Schumacher’s spokeswoman Sabine Kehm, who said he could not have been going fast “because it appears he helped a friend who had just fallen”.

But in a press conference last week, doctors who treated Schumacher said he had been skiing at great speed when he fell on December 29.

Edouard Bourgin, a specialist on accident claims, said there could have been “a catapult effect that explains the violence of the shock, even in the absence of excessive speed.”

Prosecutors are also looking at whether the limits of the ski runs next to the accident site were correctly marked and whether the rock in question was lying close enough to the piste to require some kind of protection or signage.

In addition, they are examining whether the safety releases on Schumacher’s skis operated properly in a probe aimed at determining responsibility for the accident.

Schumacher turned 45 on Friday, and fans marked the birthday with a silent vigil outside the facility, part of which was organised by Ferrari, Schumacher’s former team.

His wife Corinna and two teenage children have been at his bedside throughout, and other family members have come to visit, including his father Rolf and his brother Ralph, who is also a racing driver.

Kehm said Schumacher remains in a “critical but stable” condition after he underwent two surgeries earlier in the week to ease pressure and bleeding. No further press conferences are scheduled before Monday.