The students' demands reportedly do not concern religion or immigration, but focus instead on understaffing and lack of funding. Marine Le Pen's far-right National Rally party has not linked the protests to France's migration policy.

In Marseille and Nantes, protesters held up handmade signs bearing phrases such as "The state has killed national education." In Toulouse, parents linked arms at the front of a march through the city.

Paris police said clashes in the capital resulted from some 300 people, most hooded or masked, facing off against security forces, and that the protest generally unfolded without major incident elsewhere. Several storefronts were damaged.

The Interior Ministry said 488 people had been arrested and 48 security personnel were injured on Tuesday.

The student protests began in September in the deprived suburbs of Paris before spreading nationwide.

Students complain about schools facing basic maintenance problems, from water leaks to rat infestations.

"There is such a gap between the elites and us," said Hugo Vetzel, a recent high-school graduate in Strasbourg.

The High School Students Union said more than half of France's high schools were blockaded or had closed for the day. Some local education authorities have tried to move classes online.

Rights groups, students and parent groups have accused authorities of using disproportionate force against minors. The government says the protest movement has been hijacked by outsiders and in some places deteriorated into urban violence.

More than 1,800 people are being prosecuted for unspecified crimes, including 1,483 minors, the justice ministry said on Monday.