The act may have a religious motive. A French terrorism prosecutor said he was investigating the case.
French police said on Friday they shot a man who had killed a man a moment earlier by slitting his throat open in the suburb of Conflans Sainte-Honorine in Paris, news agencies said.
The victim was apparently a history teacher at a French high school.
Conflans Sainte-Honorine is located in the northwest of Paris. Police found a man with a knife near the scene of the attack just minutes after the incident and shot him to death, a police spokesman says.
French a prosecutor specializing in terrorism said he was investigating the case as a terrorist act.
The details of the attack are still unclear, but the motive for the act may be related to religion. According to police, the teacher had shown pictures of the Prophet Muhammad in class.
According to a Reuters police source, bystanders would also have heard the attacker shout “Allahu Akbar,” meaning “God is the greatest”. According to a police spokesman, the veracity of the information is still being checked.
The spokesman did not confirm information from another police source that the head of the school teacher had been removed.
French president Emmanuel Macron intends to visit the venue. He announced the visit after an emergency meeting of the Ministry of the Interior on Friday, French media reports BFM TV.
The publication of images of the Prophet Muhammad has also been the subject of several previous attacks in Paris.
A man who moved from Pakistan to France last month attacked two people with a meat ax outside the delivery of satire magazine Charlie Hebdon.
In the same location, another attacker shot several magazine employees five years earlier. The attacker was outraged by the cartoons published by the prophet Muhammad published by Charlie Hebdo.