Investigators do not believe Monday evening's attack in a rural area east of Paris was a terror attack.
Sources told the AFP news agency that he had taken a large amount of medicinal drugs but that his statements so far have not made it possible to establish his motives.
Earlier he was reported to have attempted suicide in Sunday and to have and decided to try again on Monday.
The 32-year-old man drove a BMW into a busy pizzeria in the village of Sept-Sorts where about 20 people were dining outside, killing the teenage girl, seriously injuring a three-year-old boy and four other people and slightly injuring eight.
Eyewitnesses say that he had tried to reverse but someone had gone behind the car to prevent him from doing so.
He has been charged with murder, attempted murder and driving under the influence of drugs.
No weapons were found in the car or in his possession.
President Emmanuel Macron tweeted his condolences to the victims and thanks to the emergency services.
Interior Minister Gérard Collomb contacted the girl's family to express his and the president's condolences and declared his "horror" at the incident in a statement.