Dozens of high schools across France were blockaded again on Monday as the government braced for another tense week of protests over school conditions and the high cost of living.

The protests come amid warnings that weeks without lessons are putting some pupils' school year and final exams at risk.

As children returned after the two-week school holiday, students' unions ignored Emmanuel Macron's call to end the lycée blockades which have been running since September and have prompted one of the biggest protest movements and social crises of his presidency.

From early morning in Paris and its suburbs, as well as in cities including Lille, Toulouse and Marseille, schoolchildren demanding more replacement teachers and repairs to buildings barricaded school entrances with wheelie bins. Police officers outside some schools attempted to drag the bins away and made arrests.

University students' unions were planning additional barricades at faculties on Tuesday. Trade unions have called for a large-scale strike on Thursday, with rail workers, teachers and private-sector employees planning to join demonstrations in cities across France to support schoolchildren's demands for better conditions and protest against the rising cost of living and low salaries.

Nathanaël Combary from the school students' union Renouveau Lycéen, who is also a member of Macron's centrist party Renaissance, said schoolchildren must keep going in their "battle of strength" with the government to push for more funding, better access to higher education and repairs to decrepit schools.

He said measures offered by the government last week to cap some class sizes and review the university applications platform were inadequate. Combary told BFMTV that protests were the only way for schoolchildren to push a government response. He said: "Democratically speaking it's a bit scandalous that we have to reach this type of situation to be heard but it's the only solution we have." The education minister, Édouard Geffray, said he feared the school year was now "at risk" for many students in their final years who had missed weeks of classes because of the blockades and would be unable to complete coursework or catch up on the curriculum for exams.

He said: "We have pupils who are sitting their baccalauréat at the end of the year who for hundreds of thousands of them have had no classes for four or five weeks if you include holidays, and for whom the school year is now at risk. And that's something that we can't allow." Geffray said the school blockades were "illegal" and his priority was for children to return to class.

In Montpellier, the Socialist senator Hussein Bourgi accused the government of "misconduct" and "provocation" after video footage showed a 53-year-old school nurse saying something to police near a school barricade before being forced face-down to the ground, handcuffed and taken into police custody. The local prefect, in charge of police operations, defended the arrest, saying the woman had insulted officers and resisted police.

The education ministry said 41 high schools were blocked across France – around 1% of the nationwide total. Students' unions put the figure at 150.

Nicolas Bonnet, of the headteachers' union SNPDEN-UNSA, said: "It's time for us to return to our job: teaching and supporting pupils." He warned that coursework, final-year exams and university applications were at risk.

He said he understood why high-school students felt the government had not offered enough to fix problems in schools, but urged more dialogue between the government and pupils.

The prime minister, Sébastien Lecornu, said he would meet school students' unions again next week.