A driver shouted "Allahu Akbar" as he ploughed into a crowd in the eastern French city of Dijon, injuring 11 people, two seriously, French media say.
He was arrested after targeting pedestrians at a number of locations.
The suspect is "apparently imbalanced and had been in a psychiatric hospital", a source close to the investigation said, adding that "for now his motives are still unclear".
The attack came the day after a French convert to Islam was shot dead after attacking three police officers with a knife while also reportedly crying "Allahu Akbar" ("God is great") in the central town of Joue-les-Tours.