PARIS — Most schools throughout France observed a minute of silence on Friday in remembrance of Samuel Paty, a teacher whose attempt to illustrate free speech to his students led to his beheading a year ago by an Islamist fanatic.
As a history teacher, Mr. Paty was responsible for teaching civics. To illustrate the right to blasphemy, free speech and freedom of conscience, he showed caricatures of the Prophet Muhammad, setting in motion a swirl of lies and rumor that ended in his beheading.
The police investigation revealed that the girl who told her father, Brahim Chnina, a false version of what had taken place in the class and prompted the online frenzy that led to the killing had not been in the class at all.
The girl told the police that Mr. Paty had questioned all students on their religious allegiance, let Muslims know that they could leave because “they would be shocked” and then ordered her out of the class for causing a ruckus while images of a naked Prophet were shown. But the story was made-up; she was never there.
The judicial investigation is continuing, and no trial is expected for at least a year.
The killing in a northern Paris suburb has had lasting effects, in part because France views schools as hallowed ground, places where citizens are forged through learning the right to question everything, accept differences, believe in God or not, and place the values of the republic above those of their particular ethnic or religious identity.
A front-page banner headline on Thursday in the French daily newspaper Le Monde — “Paty: A Lasting Trauma” — captured a sense of shock that has not entirely abated. A Samuel Paty Square in the Fifth Arrondissement of Paris will be inaugurated on Saturday.
That sense of shock was reflected on Friday as Mr. Paty’s death was commemorated across the country. A group of imams from the Grand Mosque in Paris laid a wreath outside the school where Mr. Paty had taught in Conflans-St.-Honorine.
The tensions in French society that led to the killing, however, were evident in the fact that the Education Ministry gave teachers the option of holding a debate on the beheading if they believed a minute of silence would be interrupted by heckling.
The killing of Mr. Paty by an 18-year-old Chechen refugee, Abdouallakh Anzorov, who was shot dead by the police, has intensified debate on security and immigration, radicalized politics in the run-up to the presidential election next year and prompted intense scrutiny of the French secular model known as laïcité.
In some ways, France is approaching a Samuel Paty election, dominated by the right because the left has found no answer to overwhelming concerns over security. An opinion poll published in April by the Journal du Dimanche indicated that 86 percent of French people view security as a major electoral issue, up from 60 percent a year earlier.
These are the fears that have caused an insurgent far-right TV pundit and polemicist, Éric Zemmour, to gain popularity with his anti-immigrant talk, even though he is not yet a declared candidate.
David Feutry, a history teacher at a high school in Dreux, about 50 miles west of Paris, said that since the killing of Mr. Paty, he “feels a constant mission of memory, to explain why we can criticize religion, why freedom of conscience is important and why laïcité matters.”
France is in theory a nondiscriminatory society where the state upholds strict religious neutrality. It is a nation that in its now questioned universalist self-image dissolves differences of faith and ethnicity in a shared commitment to the rights and responsibilities of French citizenship.
That was the lay model Mr. Paty tried to set out to his class, paying with his life.
But some French Muslims and other immigrants see this supposedly colorblind blueprint for a society of liberty, fraternity and equality as no more than an exercise in hypocrisy that masks widespread discrimination.
Mr. Feutry acknowledged the problems in French society. Working in a town with a large Muslim population, where the far-right National Front, now known as the National Rally, won some of its first electoral victories, he said he felt a special need to explain to Muslim students why, for example, blasphemy is not a crime in France.
“We have to acknowledge there is a problem,” he said. “The republic abandoned some of these people. If they were dumped in separate urban areas, should we be surprised that they turned toward their traditions and Islam?”
Understanding had to be built, he suggested. He finds that talking about his grandfather’s role on the French side in the Algerian war, and the role of his Muslim students’ forebears in the National Liberation Front, can be helpful by bringing out suppressed, divisive history.
“Paty was not a hero; he was a victim,” Mr. Feutry said. “My students need to understand how dangerous social media and rumor can be.”
The investigation into the killing has revealed that Mr. Chnina, through videos and Facebook, spread his daughter’s false account of what Mr. Paty had done. It was understandably false because she was not there and made up her version. This did not prevent an Islamist radical, Abdelhakim Sefrioui, from making a YouTube video based on Mr. Chnina’s work that named Mr. Paty’s school. The online storm grew — and Mr. Anzorov, the young Chechen, alerted to it, decided to buy a knife.
Because several minors are involved, and because so much of the case involves online invective intensified by rumor, the investigation has proved particularly complex.
Emmanuel Menetrey, a history teacher at a school near Dijon, in the east of France, said he had been struck with “stupor” on learning of the killing a year ago. “That to teach in France could be to risk one’s life had never occurred to me,” he said.
“The French people are strongly attached to their schools, so this was a point of rupture, for all teachers and for the nation,” he said. “Laïcité is not the answer to everything, and we should be aware of inequalities and prejudice, but it should still be the objective we try to attain.”
Mr. Menetrey, in a transquil rural school, observed a minute of silence with all students. Mr. Feutry, in the more fraught environment of Dreux, opted to engage in a debate with his class.
Mr. Paty, Mr. Menetrey said, had died because of “shameless lies spread on social media.”
A Samuel Paty amendment, adopted by the Senate this year, makes it a crime punishable by three years in prison to spread personal information that puts someone’s life in danger. It passed despite concerns that it might pose a threat to the freedom of the press.