Hundreds of young people surrounded a fire truck that had arrived to put out a blaze at Marseille's Saint-Exupery high school in the morning, police said on Thursday.
The attackers forced the firefighters to flee the vehicle, then set it alight.
The head teacher was attacked in Victor Hugo high school in the same southern city and suffered injuries, the prosecutor's office said, without going into more details.
Another blaze hit a school in the western city of Nantes, fire crews said.
The demonstrations and blockades, which began last week, have become a political flashpoint at a sensitive moment for the government, which announced a series of deeply unpopular spending cuts in its 2027 budget on Thursday.
Prime Minister Sebastien Lecornu's office held a crisis meeting on Thursday afternoon on the protests, which have left dozens of people injured.
Hundreds have also been arrested, most of them teenagers, officials have said.
In the Parisian suburb of Saint-Denis, crowds of young people massed in front of a line of police.
One student held up a sign marked with: "Can we explain ourselves without being tear-gassed?"
Students have accused the police of using heavy-handed tactics including the use of tear gas.
The government has criticised the violence that has broken out during some of the protests but has said difficulties in high schools should be acknowledged and addressed.
Interior Minister Laurent Nunez said that, in some places, troublemakers were moving from school to school to incite violence.
Education Minister Edouard Geffray called for schools to hold classes remotely if protesters were blocking their premises.
"Violence will not keep our students from their fundamental right to an education," he said in a post on social media platform X.
In Nantes, Olivier Chateau, a deputy to the mayor, told broadcaster franceinfo that the fire at Nelson Mandela high school was under control and that there had been no injuries.
People in the building had been evacuated, while students due to arrive at the school were turned away, he said.
