The video shows two policemen holding up a 15-year-old boy while another violently punches him, on the sidelines of student protests yesterday against proposed labour reforms.
The boy, attending a protest in the French capital, was lying on the ground surrounded by the police when one of them shouted at him to get up before punching him.
"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 boy told local media.
French students reacted angrily, pelting two Paris police stations with stones and setting off tear gas canisters.
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The youngsters tried to smash the reinforced windows of one station with planks of wood, while one of them also scrawled "Death to cops" on the wall, an AFP journalist reported.
Police allowed the youngsters to leave the area before stationing riot police out front.
Student protests were held across France yesterday against proposed labour reforms which saw cars torched in the capital and clashes with riot police, who responded with tear gas and made more than 30 arrests.
Dozens of the injured boy's fellow pupils gathered for a quiet demonstration today outside his Paris school.
"I was shocked," said Brelotte, 15. "The policeman's punch was too much. He was on the floor and under control, what was the point?"
The Paris prosecutor has opened an investigation into the incident.
"These images are shocking and shocked me," said Cazeneuve.
"The behaviour of the forces of order should be exemplary, irreproachable in every instant."
Paris police chief Cadot added: "If there was an error, it will be punished.
"There was no doubt provocation from the students but this doesn't justify security forces not controlling their behaviour, that is what makes the job difficult," he said.