A knifeman fatally stabbed one teacher and wounded another in an attack at a school in the northern France city of Arras on Friday and the investigation was handed to the anti-terrorism prosecutor's office.
The regional Pas-de-Calais authority said the suspected assailant was arrestedbut urged local people to avoid Arras city centre.
The suspect was a Russian-born Chechen and former student of the Lycee Gambetta high school where the attack happened, a police source said.
He was on a state watchlist of people known as a potential security risk, the police source added. The 'Fiche S' contains thousands of names and only a small number are actively monitored.
Police could not confirm local media reports that he shouted "Allahu Akbar". BFM TV reported he was about 20 years old.
"We're all in a state of shock," said philosophy teacher Martin Doussau, who was chased down by the attacker but managed to escape unharmed after locking himself down in a room.
Doussau said he witnessed the assailant going after the school's cook in the yard during a break between two classes before the attacker approached his way.
"He was looking for a history teacher," Doussau told Reuters. "That's what leaves me thinking this wasn't related to a personal problem, or about settling a personal vendetta with a teacher."
The La Voix du Nord regional newspaper reported the teacher was killed trying to stop the attacker from inflicting harm.
A second police source said there was no immediate indication of a link between the attack and the conflict between Israel and the Hamas movement.
President Emmanuel Macron was heading to Arras, his office said. In a national address a day earlier, Macronurged the French to remain united and refrain from bringing the Israel-Hamas conflict home.
BFM TV said the person killed was a French language teacher, while a sports teacher was stabbed and injured.
Pupils were confined to their classrooms, it added.
The suspected assailant's brother was also arrested.
Arras is a city in the desindustrialised, ethnically diverse northern corner of France, a region where the far right enjoys strong support.
Education Minister Gabriel Attal said security would be reinforced in schools throughout France.
France has been targeted by series of Islamist attacks over the years, the worst being a simultaneous assault by gunmen and suicide bombers on entertainment venues and cafes in Paris in November 2015.
In 2020, a teacher, Samuel Paty, was beheaded by a Chechen teenager who wanted to avenge his use of cartoons mocking the Prophet Mohammad during a class on freedom of expression.