Derek Thompson, 47, faces charges of involuntary homicide and involuntary wounding after the bus he was driving fell to the bottom of the A26 motorway embankment near Chalons-en-Champagne early on Sunday.
Tributes have been paid to Alvechurch Middle School teacher Peter Rippington, 59, after he died and his wife Sharon and daughter Amy were injured in the crash. A total of 29 pupils were involved in the crash near Rheims.
And in a statement released after a court hearing in Chalons-en-Champagne, prosecutor Christian de Rocquigny said: "The driver explained that he had no recollection of the circumstances of the accident.
"While in custody, after denying falling asleep, the driver acknowledged that it was possible that he was drowsy."
Tests have shown Mr Thompson was not under the influence of alcohol or drugs, and local police are reportedly investigating whether he may have fallen asleep at the wheel.
Mr de Rocquigny said in an earlier statement: "Witnesses who were driving in the area near the coach saw the vehicle repeatedly swerve towards the verge.
"The tachograph indicates some unexplained variations in speed in the nine minutes before the accident, the judge explained."
Mr Thompson has been allowed to go back to the UK, but must return to France to go before court when required.
The prosecutor said he must "inform the judge of any travel outside Great Britain", is banned from "contact with victims and families of these, except the other driver", and banned from "driving on French territory".
Most of the 49 British nationals who were on the coach are back in the UK, according to the Foreign Office, but seven people remained in hospital in France.
A spokesman said: "Our thoughts remain with everyone involved in or affected by the tragic bus crash in France.
"We would like to thank the French authorities and emergency services for the outstanding assistance they have provided to those involved in this tragic event."
Mr Rippington was described by Bryan Maybee, chairman of governors of Alvechurch Middle School, in Worcestershire, as a "dedicated and inspirational teacher".
And a statement from the Rippington family said: "We, as a family, are devastated at the tragic loss of Peter, a wonderful husband, father, son, brother, son-in-law, brother-in-law, uncle, friend and teacher."