A car smashed into a pizza restaurant east of Paris late Monday, killing an eight-year-old girl and badly injuring six other people.
Investigators believe the act was "deliberate... but apparently has no connection with a terrorist act," the public prosecutor's office in the town of Meaux said.
France has suffered a string of terror-related attacks, including the use of cars as weapons.
On August 9, six soldiers were injured after they were hit by a rented BMW in a western Paris suburb.
The suspect, a 36-year-old Algerian man, was later shot and wounded after a dramatic motorway chase.