The demonstrations are the latest to be held in the capital over the alleged rape and other reported police abuses.
The victim, known publicly only as Theo, reported being beaten up by officers and raped with a truncheon after being stopped on 2 February.
Four police officers have been suspended pending an inquiry.
The demonstrators set fire to bins after starting their protest at the Place de la Nation.
The protesters gathered outside schools in Paris to prevent students and teachers from entering, using rubbish bins and other objects to barricade the entrances.
There were no reports of serious injuries, despite pictures on social media of clashes between police and protesters on the fringes of the Place de la Nation rally.
Police said they carried out only a handful of arrests.
Police said the protests were unlawful because no prior permission had been granted, according to local media.
Protests are also reported by French media to have taken place in Montpelier.
Earlier this month, Theo described his trauma at the hands of police. He said he left home in north-west Paris and found himself in the middle of a police identity check targeting drug dealers.
He said he was then raped with a truncheon, as well as racially abused, spat at and beaten around his genitals.
Police have fired tear gas at Paris students who blockaded 16 high schools in protest against the alleged police rape of a young black man.