Didier Lemaire told French media the threats began after he wrote an open letter saying the state did not do enough to protect Samuel Paty, the teacher beheaded in a jihadist attack last October.
Lemaire teaches philosophy at a high school in Trappes, a low-income Paris suburb in the Yvelines département with a large Muslim population that has become emblematic of the government's efforts to curb radicalism.
Authorities say hardline Salafist conservatism has attracted a widespread following in the town, which authorities say was the home of around 50 people who left to fight alongside jihadists in Iraq and Syria in recent years.
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“We have been alerted to the worries expressed by this teacher with regards to threats he allegedly received,” the prosecutor's office in nearby Versailles told AFP, without providing details.
A police source confirmed that Lemaire was benefiting from police protection.
“In accordance with his wishes, the school district will ensure, in cooperation with the police, conditions that will allow him to continue teaching at the school,” the Versailles board of education said in a statement.
Paty's killing came as France remains on high alert after a series of terror attacks since the January 2015 massacre at the satirical weekly Charlie Hebdo, which had published controversial cartoons of the prophet Mohammed.
Paty had showed the cartoons in class as the trial began for suspected accomplices in the attack, angering parents who targeted him in a social media campaign that sparked his killing by an 18-year old Chechen man, Abdullakh Anzorov.
Writing a few weeks later in the news magazine Le Point, Lemaire wrote that “I have been a witness to the sectarianism that is taking an increased hold on people's bodies and minds”.
He said that Paty “was not protected by an institution that underestimated the threat”.