There have been a number of confrontations. Bins were set alight on the Champs-Elysées and cars were torched on Boulevard de Courcelles, about 2km (1.2 miles) north.
Water cannon were deployed on a street east of the city centre.
TV pictures have shown what appear to be far-right groups setting up barricades. Armoured vehicles are being sent to deal with them, and French media say this is the first time they have been deployed in metropolitan Paris.