Mr Chirac spoke after chairing crisis talks following the 10th – and worst – night of violence, arson and looting.
He said it was an “absolute priority” to re-establish order. But soon after, fresh unrest erupted in several cities.
In Grigny, south of Paris, rioters fired shots at police, injuring 10 police officers, two of them seriously.
Violent attacks were also reported in Orleans, Rennes and Nantes.
Unrest began after the deaths of two youths in the rundown Paris suburb of Clichy-sous-Bois, who were accidentally electrocuted at an electricity sub-station after reportedly fleeing police.