The 30-year-old was airlifted to hospital to treat a subdural haematoma on December 27 after he crashed into protective netting while training for a World Cup race in Bormio.
Sarrazin, French ski team doctor Stephane Bulle said, had been transferred to the neurological care service of a Lyon hospital "where he will launch into his rehab" which will last months.
"We're going to start allowing him to do things that everyone does, namely sit, eat, stand up," Bulle said.
"Today, he still has a little trouble opening his eyes because he suffers from diplopia," or double vision.
"He is very tired, he really has a lot of trouble communicating. When you come out of this period of coma, so to speak, you are really exhausted."
Sarrazin enjoyed his best campaign on the World Cup circuit last season, with four victories including a downhill win at Bormio.
Asked whether he thought Sarrazin could resume his ski racing career, Bulle said: "I have absolutely no idea where this is going to lead us. I can't tell you. But that's our goal anyway."
