French police arrested two men and a woman on Tuesday in connection with deadly Islamist militant attacks on Paris last month and in January, judiciary officials said.

In a separate event that highlighted the knock-on impact of tensions over Islamist violence, a teacher who claimed to have been stabbed by a man on Monday acting in the name of Islamic State militants was hospitalized after admitting to police that he had invented the story, prosecutors said.

Islamic State, which claimed responsibility for the Nov. 13 attacks, has stated that teachers in France's secular state-schooling system should be killed for promoting what it called the evils of secular life, music and drawing.

France remains on top security alert since at least eight gunmen and suicide bombers killed 130 people at cafes, a concert hall and near a sports stadium in Paris on Nov. 13 - the deadliest attack on French soil since World War Two.

One of the two men arrested on Tuesday in Villiers-sur-Marne to the east of Paris was deemed a "peripheral" suspect in the investigation into the Nov. 13 attacks, judiciary sources said.

Seven assailants died in that attack and an eighth in police raids days later, but police are still searching for another chief suspect, Salah Abdeslam, who vanished after escaping to Belgium from Paris.

Another man and a woman arrested by police on Tuesday were suspected of supplying weapons to Amedy Coulibaly, who killed a policewoman and then four other people at the kosher store on the eastern edge of Paris last January, they said.

That attack took place on the heels of another in which two Islamist militants killed 12 people at the offices of the satirical newspaper Charlie Hebdo, which became a target after publishing mocking cartoons of the Prophet Mohammad.

(Reporting by Chine Labbe; Writing by Brian Love; Editing by Mark Heinrich)