|The gendarmes set up a roadblock at the scene in Sept-Sorts, east of Paris|
The driver of the BMW, which hit an outdoor terrace at the restaurant in Sept-Sorts, has been arrested, according to the national gendarme service.
Authorities initially said the girl was eight years old, but later said she was 13. Her younger brother was among those injured.
|The male driver of the car is believed to have been suicidal|
Pierre-Henry Brandet, a spokesman for the French Interior Ministry, said first indications were that it was not terror related and that the male driver is believed to have been suicidal.
Mr Brandet told BFM television four of those injured were in a condition of "absolute emergency". Eight others were slightly injured.
Last week, an Algerian man was arrested after he drove his car into a group of French soldiers, injuring six.
Eighty-six people were killed in Nice in July last year when a truck drove through crowds celebrating Bastille day.