French ministers have made keeping schools open a priority, despite a recent surge in Covid-19 cases, fuelled by the Omicron variant.
Teachers say Covid rules in school are confusing and constantly changing..
The government said almost 40% of primary teachers and 24% of secondary teachers had walked out on Thursday.
But those figures were well below estimates by unions, which said they expected about 75% of primary teachers to go on strike.
The top Snuipp-FSU union said it expected one in two primary schools to close on Thursday in a "historical mobilisation" of teachers on a scale not seen in decades.
The nationwide strike was organised by 11 unions representing teachers, parents and other school staff.
In cities across France on Thursday, teachers took to the streets to vent their anger at the government's Covid policies.
"We had reached such a level of exasperation, tiredness, and anger that we didn't have any other option but to organise a strike to send a strong message to the government," said Elisabeth Allain-Moreno, national secretary of the SE-UNSA teachers union.
Some parents said they sympathised with and held no grudge against teachers who had walked off the job.
Outside a school in north-east Paris, one parent, Akim Aouchiche, told the AFP news agency that "classes are too big, they don't get paid enough, their working conditions aren't the best".