The protests closed a number of schools in Paris, with roughly one in 10 teachers taking part, France 24 reported.
Organisers say the health of both students and teachers is at risk due to insufficient protocols to protect against the virus. Crowded classrooms and canteens make social distancing difficult, they say.
The protests came a week after riot police pepper-sprayed students who blockaded a Paris high school in protest over inadequate sanitary measures.
The education ministry has sought to allay concerns by allowing secondary schools to offer more online teaching, on the condition that pupils take at least 50 percent of classes at school.
But teachers’ unions say the government must urgently hire more staff so that classes — which average more than 30 pupils — can be split into smaller groups and spread out to ensure social distancing.
Not all unions took part in the protests, and several parent associations also want students to continue in-person learning.
Schools were among the first to shut during European countries' first lockdown in the spring, but most governments have opted to keep them open this time.
In France, the education ministry has put in place a raft of rules including compulsory masks for all teachers and pupils from the age of six.