Islamic State's French-language magazine Dar-al-Islam last month urged followers to kill teachers in France, describing them as "enemies of Allah" for promoting secularism.
The country remains on high alert following the November 13 terror attacks in Paris that left 130 dead, and Rachel Schneider, of the French primary school teachers' union SNUipp, said many teachers had been alarmed by the threat.
She said: "We have received many calls from colleagues, who are very worried.
"They don't necessarily think there will be an organised attack, but they fear this message of murderous madness will inspire unstable people to action."
