A young man “had his hand blown off by a grenade” in Saint-Étienne, the south-eastern city’s Mayor Régis Juanico said on social media, adding: “Such a tragedy should never have happened.”
The interior ministry said the protests involved “targeted acts of violence” from “hooded individuals” in places, including parts of the capital and also Marseille, Rennes, Toulouse and Angers.
Damage to buildings was reported across France, including in Grenoble, Avignon, Pau, Montpellier and Valence.
Clothes and food shops were raided in Paris, while an Apple store in Lille was broken into and emptied.
Footage authenticated by BBC Verify showed a tourist train in Grenoble being driven by masked men along a narrow street in the city centre towards at least three riot police officers.