DEMONSTRATIONS have taken place across France in support of freedom of speech and to pay tribute to a history teacher who was beheaded near Paris after discussing caricatures of Islam's Prophet Muhammad with his class.

Samuel Paty was decapitated on Friday by an 18-year-old Moscow-born Chechen refugee, who was then shot dead by police.

Political leaders, associations and unions rallied in Paris and other major cities including Lyon, Toulouse and Bordeaux.

The gatherings came as French authorities said they have detained an 11th person following the horrific attack in Conflans-Sainte-Honorine, north-west of Paris.

French anti-terrorism prosecutor Jean-Francois Ricard said an investigation for murder with a suspected terrorist motive has been opened.

At least four of those detained are family members of the attacker, who had been granted a 10-year residency in France as a refugee in March, was armed with a knife and an airsoft gun, which fires plastic pellets.

His half-sister joined the Islamic State group in Syria in 2014, Ricard said. He did not give her name, and it is not clear where she is now.

A Twitter account under the name Abdoulakh A belonged to the suspect. It posted a photo of the decapitated head minutes after the attack along with the message "I have executed one of the dogs from hell who dared to put Muhammad down".

The attack has upset moderate French Muslims, with a group of imams in the Lyon region holding a special meeting on Sunday to discuss what the group called "the appalling assassination of our compatriot by a terrorist who in the name of an uncertain faith committed the irreparable".