French police on Monday launched a series of raids targeting extremist networks three days after the beheading of a history teacher who had shown his pupils a cartoon of Prophet Mohammad.

The operation came a day after tens of thousands of people took part in rallies countrywide to honour history teacher Samuel Paty and defend freedom of expression, including the right to show cartoons regarded by many Muslims as insulting.

Gerald Darmanin said "dozens" of individuals were being probed for suspected radicalisation.

While they were "not necessarily linked" to Paty's killing, the government aimed to send a message that there would be "not a minute's respite for enemies of the Republic", he added.

Darmanin said the government would also tighten the noose on NGOs with suspected links to extremist networks, including the Anti-Islamophobia Collective.

The collective, which gathers data on anti-Muslim attacks, on Monday accused the minister of slander.

"Fear is about to change sides," President Emmanuel Macron told a meeting of key ministers Sunday to discuss a response to the attack.

"Islamists should not be allowed sleep soundly in our country," he said.

Paty, 47, was attacked on his way home from the junior high school where he taught in Conflans-Sainte-Honorine, 40 kilometres northwest of Paris.

A photo of the teacher and a message confessing to his murder was found on the mobile phone of his killer, an 18-year-old Chechen man Abdullakh Anzorov, who was shot dead by police.

The grisly killing has drawn parallels with the 2015 massacre at Charlie Hebdo satirical magazine, where 12 people, including cartoonists, were gunned down for publishing cartoons mocking Prophet Mohammad.

According to his school, Paty had given Muslim children the option to leave the classroom before he showed the cartoon in a lesson on free speech, saying he did not want their feelings hurt.