It all began when a high-school teacher warned that Islamists had taken over the city. The teacher went on TV, issuing alarms from inside what he called a “lost city” of the French Republic. In Trappes, he said, he feared for his life.

“Trappes, it’s finished,” the teacher said. “They’ve won.”

The mayor, a strong believer in the Republic, saw the teacher on television and didn’t recognize the city he described. He knew his city, west of Paris and with a growing population of immigrants and Muslims, had problems but thought it was being falsely maligned. The mayor also happened to be a Muslim.

“The truth doesn’t matter anymore,” he said.

For a few weeks this winter, the fight pitting the mayor, Ali Rabeh, 36, against the teacher, Didier Lemaire, 55, became a media storm that, beneath the noise and accusations, boiled down to a single, angry question that runs through the culture wars rippling through France: Can Islam be compatible with the principles of the French Republic?

No setting was perhaps more potent than Trappes to debate that question. It is a crucible of France’s hopes, and fears. Trappes gave birth to some of the country’s brightest entertainment and sports stars, like Omar Sy, the lead actor in the recent Netflix hit “Lupin.” But Trappes also saw about 70 of its youths leave for jihad to Syria and Iraq, the largest contingent, per capita, from any French city.

The confrontation between teacher and mayor reflected broader forces reforging a society where French identity is being questioned more than ever. As his positions on Islam hardened following terrorist attacks in France in recent years, the teacher, like many others, moved further to the right politically.

Mr. Rabeh, the mayor, belonged to an outspoken generation, unafraid to express its identity and point out France’s failings, whose immigrant parents had preferred to pass unnoticed. He took for granted his role in France — and Islam’s place in it.

The fight became personal, as the teacher, saying his life was in danger, accused the mayor of calling him a racist and an Islamophobe. {snip}

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One evening in February, Le Point, a major conservative newsweekly, posted an article about Mr. Lemaire, who said he was quitting because of Islamists.

Within a few hours, a conservative politician eyeing the presidency tweeted her support for Mr. Lemaire and “all those hussars on the front line in the fight for the Republic.” Next, the far-right leader, Marine Le Pen, attacked “certain elected officials” for failing to protect the teacher from Islamists.

That the words of a virtually unknown teacher resonated so much was a sign of the times. A few months earlier, an extremist had beheaded a middle-school teacher for showing caricatures of the Prophet Muhammad in a class on free speech. President Emmanuel Macron was now pushing a bill to fight Islamism even as he pledged to nurture an “Islam of France.”

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In the article, Mr. Lemaire said he had been under police escort for months. Trappes’s mayor, he said, had called him an “Islamophobe and racist.” He said he was waiting for an “exfiltration” from deep inside “a city lost for good.”

Overnight, the soft-spoken, longhaired teacher, who said he preferred curling up with Seneca than going on Facebook, was issuing dire warnings on top television news shows.

“We have six months to a year,” he said, “because all these youths who are educated with the idea that the French are their enemies, they’ll take action one day.”

Mr. Lemaire arrived in Trappes, a banlieue, or suburb, in the outer orbit of Paris, two decades earlier. Once a village that grew around a millennium-old Roman Catholic parish, Trappes is now a city of 32,000.

Mr. Lemaire’s high school, La Plaine-de-Neauphle, stands at the heart of an area built to accommodate immigrant workers from France’s former colonies in the 1970s — a mixture of rent-subsidized high-rises, attractive five-story residences and a constellation of parks. The mosque is nearby. So is a market where vendors offer delicacies from sub-Saharan Africa and halal products.

When the immigrants first came, community associations funded by the government provided support and services. But by the time Mr. Lemaire arrived, social programs had been slashed. Factories were laying off immigrant fathers and offering no jobs to their children. One crime-ridden neighborhood became known as “Chicago.”

In an interview with The New York Times, Mr. Lemaire said he took seriously his mission as a hussar instilling France’s values in the classroom.

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But the spread of Islamism complicated his work, he said. His students increasingly challenged what he taught. Some, he believed, considered him an enemy, while others hid their radical beliefs.

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But the teacher said he began truly grasping the Islamist threat only after the series of terrorist attacks in France in 2015. He took a first step in 2018, writing a letter to Mr. Macron saying the president needed to take Islamism more seriously.

In January, he joined a tiny political party, Parti républicain solidariste, which espouses a hard line on France’s version of secularism, called laïcité. He now favors taking girls away from their parents, after a second warning, if the children violate laïcité rules by putting on Muslim veils during school field trips.

“We have to protect children from this manipulation,” of being used “as soldiers or as ideologues,” he said.

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To Mr. Rabeh, the teacher’s comments were tantamount to dismissing another generation from the banlieue.

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He grew up in another banlieue, near Trappes. His father had been an immigrant from Morocco who worked 38 years on Peugeot’s assembly lines.

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Most stinging was the teacher’s depiction of Trappes as a “lost city.” Over the years, the right and far right had turned “lost territory of the Republic” into a coded phrase alluding to areas with Muslim immigrants where the government’s authority had supposedly collapsed because of Islamists and criminals — a reverse colonization on French soil.

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A week after the teacher’s comments first went public, the mayor wrote a letter to the students at the teacher’s high school.

“Don’t let anybody ever tell you that you’re worth nothing and that you’re lost to the Republic,” he wrote.

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Until that day, Mr. Macron’s ministers had remained quiet but they were facing intense pressure from conservative politicians and media outlets to support the teacher.

As it happened, a televised debate was scheduled that evening between Ms. Le Pen and Gérald Darmanin, the interior minister leading the government’s crackdown on Islamism. Hours before the debate, he announced that the teacher would be granted police protection.

That evening, Jean-Michel Blanquer, the national education minister, issued a statement supporting the teacher. He also accused the mayor of trespassing into the high school to distribute tracts — the letter — that morning. “Political and religious neutrality is at the heart of the operation of the School of the Republic,” the minister said.

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The teacher was forced to leave the school where he had taught for 20 years and, despite his criticisms of Trappes, said “you really feel you’re on a mission.” He said he should have been more careful with the facts and had made “many mistakes,” but stuck by his interpretation of Trappes as “lost.”

His words, he said, had led to a “clarification of positions today in France.”

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