Some 2,000 demonstrators gathered in Bobigny, near Aulnay-sous-Bois where the alleged assault took place, to demand "Justice for Théo", the 22-year-old who is still in hospital after the alleged assault 11 days ago.
Many held placards declaring "Police rape" and "Police kill innocent people".
Despite the organisers' appeal for calm, a number of youths - dozens according to press reports, hundreds according to police - attacked local authority buildings, pelted police officers, set fire to cars and attacked two vehicles belonging to media organisations.
The police, who say they saved a child from a burning car, fired teargas and the demonstration dispersed.
Thirty-seven people were arrested.
Demonstrations in other towns
Smaller demonstrations took place in several other towns - 300 in the eastern city of Nantes, 250 in the south-western city of Toulouse, 200 in Rouen in Normandy.
Bus shelters and a gendarmes' barracks were attacked and bins set of fire in Rouen, where two arrests were made, according to officials.
Four officers have been suspended and one has been charged with rape, although an initial police investigation concluded that there was insufficient evidence to prove that the assault was not accidental.