Fires were set in the streets as high school students and others protested a shortage of teachers, overcrowded classrooms and deteriorating school buildings, BBC reported.
The protests began in Paris last week before spreading nationwide, affecting cities including Montpellier, Nantes and Marseille.
French Justice Minister Gerald Darmanin said the situation had “gone from high-school student demonstrations to a public order disturbance.”
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In Belfort in northeastern France, a 17-year-old was arrested on suspicion of attempted homicide following protests in which a police officer was targeted.
BBC Verify authenticated two videos showing the man, later identified by a minister as a police officer, being attacked near a school in Belfort.
The graphic footage shows a group of young men chasing the officer before he falls to the ground and is repeatedly punched and kicked in the head.
At least 65 education staff members have been injured during the unrest, the Education Ministry said.
In the Paris suburb of Pantin, police charged at protesters and made arrests after officers were targeted with projectiles.
In Strasbourg, police used tear gas amid concerns that the situation could become more hostile, according to Reuters.
Police also released images of items seized from demonstrators, including petrol bombs, an axe and so-called mortar fireworks.
The Education Ministry said school facilities had suffered “significant damage” following attacks on gates, entrances and fences.
Nelson Mandela High School in Nantes sustained more than €2 million (£1.7 million) in damage, according to the regional government, after a fire destroyed its glass entrance and parts of the interior.
The blockades and demonstrations began last week before spreading to hundreds of schools across France.
Students have complained that school days are too long, classrooms are excessively hot and too many staff members are absent.
The unrest comes at a politically sensitive time for French President Emmanuel Macron, six months before next year’s presidential election.
