The incident occurred with the nation still on edge a month after gunmen and suicide bombers killed 130 people in Paris in an attack claimed by Islamic State, the jihadist group that has seized large areas of Syria and Iraq and is now the target of air strikes by a US-led coalition including France.
"(The teacher) is being interviewed with a view to establishing the reasons for this invented story," said an official from the Paris prosecutor's office.
Earlier on Monday, other French officials told how the teacher had reported that a hooded man claiming a link to Islamic State had assaulted him with a knife-like weapon as he prepared for classes in a school in Saint-Denis, on the northern fringes of Paris.
In recounting the teacher's story earlier, district Prefect Philippe Galli told reporters it was too early to draw conclusions about the character of the attack, noting that the assailant, wearing a balaclava, had apparently found a boxcutter and a pair of scissors on the school premises.
The teacher was taken to hospital after the alleged attack, which triggered an investigation by anti-terrorism officials.
In a recent French-language publication, Islamic State denounced France's state school system and urged readers to kill its teachers because they promoted what it called the evils of secular learning, music and drawing.
