A left-wing French politician has been arrested over a tweet apparently celebrating the death of a policeman who was hailed a hero after he took the place of a hostage and was killed by a Daesh militant.

Police arrested Stephane Poussier at his home in Dives-sur-Mer, northwest France, on Sunday after he sent two tweets welcoming the death of Lieutenant-Colonel Arnaud Beltrame.

"Whenever a policeman is shot... I think of my friend Remi Fraisse," Poussier said on Twitter, referring to an environmental activist killed by a stun grenade fired by police during a 2014 protest over a dam. "And this time it was a colonel, great! Additionally, it means one less Macron voter," he added.

Beltrame was shot and stabbed to death after offering himself in exchange for a woman being used as a human shield by Radouane Lakdim who had already killed three other people in a rampage on Friday. A national tribute is to be held for Beltrame, who President Emmanuel Macron said had "died a hero."

Poussier's remarks provoked strong reactions and his Twitter account was disabled.

"Stephane Poussier is in custody since 11:30 a.m. this morning for justifying acts of terrorism after comments published yesterday on his Twitter account," local prosecutor David Pamart confirmed to Agence France-Presse (AFP) late Sunday. He could face up to seven years in prison and a fine of 100,000 euros ($124,000).

Poussier stood unsuccessfully in elections last year as a candidate for the La France Insoumise (France Unbowed) party of radical left-winger Jean-Luc Melenchon. His comments were condemned by the party and Melenchon, who said on Twitter that it would on Monday file a complaint against him for justifying terrorism.