A teacher was killed in a knife attack in 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, who also wounded a second teacher and a school security guard in the attack, was arrested.
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 watchlist of people known as a potential security risk, the police source added.
According to BFM TV report, the 20-year-old attacker killed a French language teacher and injured a sports teacher.
Pupils were confined to their classrooms, it added.
President Emmanuel Macron was heading to Arras, his office said. In a televised address to the nation on Thursday, Macron urged the French to remain united and refrain from bringing the Israel-Hamas conflict home.
Nothing so far pointed to a link with events in Israel and the Gaza Strip, a second police source told Reuters.
France's anti-terrorism prosecution office said it was opening an investigation into the attack. The suspected assailant's brother was also arrested.
La Voix du Nord newspaper said that pupils in all schools in Arras - a town in the desindustrialised, ethnically diverse northern corner of France - were being held in their classrooms for their own safety.