AFP journalists reported scuffles between police and protesters in the afternoon, after hours of calm, as police used stun grenades and tear gas to disperse marchers in the centre of the French capital.
Some protesters threw bottles and other objects at police and set fire to vehicles, safety barriers and bins.
Between the two major squares of Bastille and Republique the damage done had been considerable, said Emmanuel Gregoire, deputy mayor of Paris, told AFP.
"The violence has to stop!" he added.
Across France, the authorities mobilised more than 60,000 police officers and paramilitary gendarmes to try to contain what they feared would be a surge in violence similar to the March 16 riots that wrought havoc along the Champs-Elysees.