Footage from Michael Schumacher's helmet camera shows him travelling at the speed of "a very good skier on fairly hard terrain" when he hit a rock and fell, investigators say.
Investigators probing into the former F1 driver's ski accident said he was eight metres off-piste when he crashed.
They said the 45-year-old "did not really look at reducing his speed when he went off piste".
Mr Schumacher suffered a severe head injury in the 29 December accident.
He is currently in a medically-induced coma at a clinic in Grenoble where doctors describe his condition as critical but stable.
Fans gathered outside the hospital on 3 January to mark the racing legend's 45th birthday.
Speaking at a news conference in the French city of Albertville, the investigating team said they had so far attended the scene of the accident in the resort of Meribel, spoken to witnesses and the medical team.
They had also examined the driver's helmet and skis and viewed footage filmed on a camera attached to his helmet.
Lead prosecutor Patrick Quincy said Mr Schumacher had deliberately chosen to go off piste, an area between a red and blue piste that was clearly signposted.
The off piste area was clearly signposted at the Meribel ski station, he said.
"[Mr Schumacher] is evidently an extremely good skier, but one of his skis hit a rock that was sticking out... it caused him to fall and he hit head on the rock," the prosecutor said.