The man had claimed that the attack had been carried out on Monday morning out the front of the Jean Perrin d'Aubervilliers school, reported TF1 radio.
The teacher said that the attacker had yelled "That's for Daesh, this is a warning", the paper reported. Daesh is another name for Isis.
The news prompted France's education minister to announce that the government would be stepping up security at schools across the country.
The story was spread far and wide, not least considering that France is on a high state of alert after the terror attacks of November 13th which left 130 dead in Paris.
Just days after those attacks a Jewish teacher was stabbed by three attackers in the city of Marseille, who were shouting anti-Semitic obscenities and expressing support for the Islamic State group, local authorities said.
Last month's attacks saw France impose a three-month state of emergency, and led to a Europe-wide manhunt for suspects who may have been involved.
Education Minister Najat Vallaud-Belkacem said the terrorist threat was "real and permanent (and) all public places deserve protection, particularly schools".
"We will continue to reinforce security measures at schools in a context where schools feel threatened," she said.