The French president is urging the public not to panic, after a knife-wielding French convert to Islam was shot dead while attacking three police officers.

A day later a motorist ploughed his car into pedestrians, screaming "god is great" in Arabic as he ran them down.

France correspondent Catherine Field says that prompted widespread panic and thoughts of terrorism, but it's more likely the pair had psychological problems.

President Francois Hollande has issued a statement at this morning's cabinet meeting, calling for vigilance in the wake of the incidents.