A psychiatric examination found the 32-year-old was not suffering from impaired judgement when he rammed a BMW into a pizza restaurant in a village near Paris on Monday evening, killing the 12-year-old girl and injuring 12 other people, including her three-year-old brother.
He has been charged with murder and attempted murder and prosecutors have asked for him to be kept in detention.
The life of another victim, a 44-year-old woman, was still in danger on Wednesday morning, while six others were still receiving emergency care, according to Paris hospital officials.
They said that 25 others had been psychologically harmed by the attack.
Terrorism ruled out
Earlier public prosecutor Dominique Laurens had said the driver, a security guard on sick leave because of an accident at work, was suffering from "serious psychological problems".
On Tuesday her deputy, Eric de Valroger, said that questioning him was proving difficult because his statements were "incoherent".
At the time of his arrest, the driver said he had taken a large quantity of drugs, which has since been confirmed by a urine test, and had tried to kill himself the previous day.
Although he had a drunk driving conviction dating from 2010, alcohol tests proved negative this time.
Terrorism has been completely ruled out as a motive.