Witnesses said he hit a barrier on his first two attempts to plough into worshipers, before heroic motorists blocked his way.
The car struck a red Renault Clio before speeding off.
A witness told Le Parisien: "People did not yell, everyone remained calm.
"We saw the car go three times around the mosque, it was strange and all of a sudden it went very fast. It was clearly trying to knock down pedestrians."
Terrorists have driven into crowds in horrific attacks in Nice, Berlin and London, and last week a man was arrested after a van ploughed into crowds outside a mosque in Finsbury Park, North London.
Paris is in a state of high alert after a series of atrocities, including co-ordinated attacks in November 2015, which killed 130 people.
Among the sites targeted by jihadists were the Bataclan concert hall, where 89 people were gunned down.