The outrage stems from a day earlier when a policeman was caught on video punching a 15-year-old boy on the sidelines of a student demonstration against the government's proposed labour reforms.
In the video, the boy is seen lying on the ground when an officer shouts at him to get up. Two policemen then hold him up, while a third suddenly punches him in the stomach.
"We were protesting, throwing eggs. A policeman ... charged at me, hit me to the ground then he told me 'get up, get up' and he punched me ... my head was spinning," the shocked boy told local media afterward.
Both Interior Minister Bernard Cazeneuve and Paris police chief Michel Cadot described the images as "shocking."
The Paris prosecutor has opened an investigation into the incident.
French students on Friday reacted angrily, with some of them pelting two Paris police stations with stones and setting off tear gas canisters. The youngsters alos tried to smash the reinforced windows of one station with planks of wood, while one had also scrawled "Death to cops" on the wall.
Police allowed the youngsters to leave the area before stationing riot police out front.
Police 'at the end of their tether'
Two policemen were injured in the chaos.
Police in France saw an unprecedented surge of support in the wake of jihadist attacks last year.
But questions over the rough treatment of people who have been subject to counter-terrorism raids had already started to reduce sympathy, and the resumption of strikes and protests over a number of government policies has put French police back in the firing line.
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Nicolas Comte, secretary general of the SGP police union, told BFM TV that many police officers were fraying at the edges in France after months of protests and the constant terror threat.
"The two issues should not be linked, but with all that has happened, in terms of protests and the terrorist threat, my colleagues are very tired and at the end of their tether," he said.
"I am not excusing it but this could explain things," he said.
Tensions between youths and police provoked violent riots across France in 2005.