One person died in Marseille after a car crashed into people waiting at two different bus stops in the southern French port, police sources told French media.
The suspected driver, reportedly a 35-year-old man known by authorities for petty crimes and mental health problems, was arrested shortly afterwards.
A man was left seriously injured.
Yves Lefebvre, of the Unité SGP Police FO union, said: "It clearly looks like a deliberate act".
Judicial police in Marseille and Lyon launched an investigation. "There is no evidence enabling [us] to qualify this as a terrorist attack," said Xavier Tarabeux, the Marseille prosecutor, adding that the "psychiatric line" was the most probable.
BFM TV cited police sources as saying that at 9.15am, a white utility vehicle, which had been stolen on Monday morning, rammed a bus stop in the 11th arrondissement of Marseille, wounding a man in the legs.
A few minutes later, in the 13th arrondissement, the same vehicle rammed another bus stop and slammed into a 40-year old woman who died on the spot.
A witness managed to take down the number plate and police seized the driver shortly afterwards. He was reportedly known for petty crimes, but unknown to French intelligence. Sources close to the investigation said he has "known mental health problems".
Police have locked down an area around Marseille's old port.
According to Le Parisien, the suspect, who is not from Marseille, was known to police for "theft, violence, bearing arms and 'dining and dashing' [leaving restaurants without paying]".
Source: News Agencies, Edited by website team