The driver is reported to have 'rammed' people eating outside the Pizzeria Cesena - said to be popular with families on a hot summer's evening - in La Fierté sous-Jouarre, killing a 13-year-old girl.
One of the seriously injured is reported to a three-year-old boy who is critical - possibly the younger brother of the teenager who died.
The 32-year-old man is reported to have also had weapons in his car when he 'drove up to the restaurant, waited outside and then driven at the restaurant at speed', according to witnesses who said there were about 20 people inside at the time.
Pictures from the pizzeria show chaotic scenes, with the grey BMW buried inside the front of the restaurant - and chairs and tables upturned and metal supports bent out of shape.
Anti-terror offices have swarmed the scene following the crash - but early indications are that while the driver intended to commit suicide, it was NOT a terror attack, according to local police.