Ralf Schumacher has been allowed home following his US GP crash but has been ruled out of testing this week.
Schumacher has flown back to Salzburg to recover from back injuries suffered when his BMW Williams hit a wall on the fastest part of the Indianapolis track.
"Ralf is well but has a bruised back and strained back muscles. He will not be taking part in scheduled testing in Jerez," said a Williams statement.
The team admit there is a "question mark" over his French GP chances.
Last year he was ruled out of the Italian GP after sustaining concussion during a test session
BMW Motorsport director Mario Theissen said: "I cannot say what will happen now. It has to be his own decision. He has to decide what to do.
"I'm not an expert and I cannot evaluate whether it's a risk or would be damaging for him to drive, but it's two major accidents for him in a year now.
"Obviously, we all hope he recovers quickly and if he is ready to race, then he will do so, but if not then we will have to see what to do."
Theissen feels the whole team is in the spotlight after what boss Sir Frank Williams described as "another bad weekend."
Williams' woes were compounded when Juan Pablo Montoya was disqualified for the second successive race, this time for leaving it too late to switch to his spare car.
Thiessen was critical that race officials waited until 16 laps from the end of the race to black flag Montoya.
"We would have preferred to have known immediately what was going on," he said.
"It happened prior to the formation lap, so there was plenty of time before the start and during the race to declare it was not correct.
"But sometimes things happen which shouldn't happen and you have to get over them and learn from them, and especially you have to take care you do not become
demotivated because of them.
"I think these are the moments the team can show it is really strong and I certainly expect us to overcome this situation and to press ahead with the developments we have running.
"We showed in Montreal, and here too, the car is coming and I am quite confident we will make progress in the coming races and overcome this situation."