Row over teacher's 'Islamism' claims in Paris suburb
Both men are now under police protection.
Didier Lemaire penned an open letter last November accusing the state of underestimating the Islamist threat.
He was writing in reaction to the killing of fellow teacher Samuel Paty, who was attacked in the street and beheaded after he showed students controversial cartoons of the prophet Mohammed.
As lawmakers began debating a controversial new bill to clamp down on extremism, Lemaire said that he now required police protection at his school.
But Trappes' mayor Ali Rabeh angrily rejected Lemaire's "lies", saying the teacher had never received any "serious threat".
On Thursday, Rabeh went to the teacher's high school to distribute letters pledging his support to students "shocked and wounded" by Lemaire's comments - prompting an uproar among some rightwing politicians who denounced an "intrusion".
On Saturday, prosecutors opened an inquiry into alleged death threats and racist insults against Rabeh, who has confirmed that he is also now under surveillance by police.
Trappes has produced soccer star Nicolas Anelka and the actor Omar Sy, star of the hit series "Lupin".
But the city is also notorious for being the home of dozens of people who left to fight as extremist militants in Syria and Iran in recent years.
Authorities say hardline Salafist conservatism has attracted a widespread following among its 32,000 residents, making the city a test case for the government's efforts to curb Islamic radicalism.
The legislation under debate in parliament would tighten rules on issues ranging from religious-based education to polygamy. Those proposals are in addition to already existing bans on wearing the niqab, or full-face veil, in public settings and the headscarf in schools.
It is a response to a series of extremist terror attacks in France that have killed more than 250 people since 2015.
Opponents accuse the French government of endemic Islamophobia.
France witnessed a 53 percent increase in anti-Muslim attacks in 2020 compared with 2019, according to the National Observatory of Islamophobia in France.
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