The vehicle was dragged for several hundred metres after being struck by a Paris-bound train at  Conde-sur-Huisne in the Orne region on Friday evening.
Deputy prefect Pascal Vion said the car "seemed to have stopped in the middle of the tracks" before the crash at 20:20 local time (18:20 GMT).
A woman managed to escape from the car prior to the collision.
None of the 34 passengers on the train, which was travelling from Le Mans to the French capital, were hurt, AFP news agency reports.
Three people have died after a train hit a car on a level crossing in the north-west of France, officials say.