The vehicle took off after the incident, which took place at about 8.00 am (1130 IST) in the northwestern suburb of Levallois-Perret.
Police described the incident as an "apparently deliberate act".
An 18-year-old with a history of psychological problems was arrested on Saturday at the Eiffel Tower after brandishing a knife.
He told investigators he wanted to kill a soldier, sources close to the case told AFP.
In June, a 40-year-old Algeria doctorate student who had pledged allegiance to the Islamic State group attacked a policeman with a hammer outside Notre Dame cathedral.