A number of vehicles were set on fire on Saturday, December 29, near the Le Parisien newspaper building in Paris.
It was initially unclear who had torched them and whether it was directly linked to France's "yellow vest" protests.
The demonstrators kept numerous roads across the country blocked as groups of protesters marched in city centers on Saturday.
In Paris, where protests turned violent in early December, police said by early evening that they had detained some 57 people after 800 demonstrators took to the streets, down from at least 109 arrests last week with a similar number of protesters.