The incident at around 10.15pm local time in the city of Caen was not thought to have a terrorist motive, the deputy prosecutor said.
It left seven people in a critical condition and three with minor injuries, according to local prefect David Claviere.
The ramming is thought to have occurred after a fight, a police source said, with Claviere saying the car “deliberately drove into pedestrians in the street opposite the train station”.
The suspect, a 26-year-old man born in Russia, was not known to intelligence services but was known to the police “only for traffic offences”, Claviere said.
He fled the scene but was later apprehended in Ouistreham, around 20km away, the police source said.
All of the victims seemed to be men aged between 17 and 40, Bruno Coutanceau, a top security official for Caen, told AFP.
Police had opened an investigation on charges of murder and aggravated assault, according to the deputy prosecutor.
“For the moment, we are not dealing with a terrorist motive, but the investigation are only just beginning,” he said, declining to give details on the deceased man’s identity.