The incident occurred around five o'clock on Friday near a school in the suburb of Conflans Sainte-Honorine northwest of Paris.
Prosecutors in the French anti-terrorism operation have been involved in the case and are investigating the attack.
According to French police, the person has had his entire neck cut off.
The suspected perpetrator, who according to French media is 18 years old, has subsequently threatened the police with a knife-like object.
He was shot by police and died.
Police tell Reuters that the victim was a teacher.
The crime is being investigated as "a murder linked to a terrorist organization", according to the prosecutor's anti-terrorism unit.
According to unconfirmed reports to the French newspaper Le Parisien, the victim had recently given a lesson in freedom of speech and shown caricatures of the Prophet Muhammad.
During the evening, the French Minister of Education Jean-Michel Blanquer said that the attack on the teacher is an attack on the country.
"France will stand strong against the monstrous Islamist terrorism," Blanquer said in a statement, Reuters reports.
The country's president Emmanuel Macron is in place in Conflans Sainte-Honorine.