The video (see below) dates back to July 2013 but was only posted online this week.
The shocking images, filmed through a body camera worn by a policeman, show the arrest of a man in Place de la Nation, south east Paris.
Details around the arrest remain unclear, but it appears the man was already injured from a preceding incident.
Police surround the man, who is clearly agitated and resistant to being arrested. After confronting the police, he goads an officer and tells him to taser him. He is then hit with a baton around the legs by another officer.
Then the policeman wearing the camera decides to use his taser to fire an electric shock at the man. But at the same time a colleague pulls out a tear gas canister and also targets him. The highly flammable combination of electric charge and tear gas results in the man being briefly engulfed in a ball of flames.
(Warning: The images may shock some viewers)
The officer with the taser panics and repeatedly shouts and swears at his colleagues: "Guys don't use gas! Who fucking gassed him?"
The man lies in pain on the ground and shouts and screams until the end of the video as the policeman tries to calm him down.
The video was published on Facebook on Tuesday before being deleted. However it was then copied and uploaded to Twitter and then picked up by French media sites.
A spokesman for French police told LCI news that the man was not seriously injured in the scuffle. It is understood an internal police investigation was launched but no officer was handed any punishment over the incident.
According to reports it wasn't the first time French police had ended up burning a man they were trying to arrest by firing a taser and tear gas at the same time. A similar incident occurred six months earlier in the northern city of Rouen.
The video emerges at a sensitive time in relations between French youths and police, who are regularly accused of brutality and using excessive force to arrest suspects.
Another amateur video published earlier this month appears to show an officer punching a scooter rider as he tries to arrest him, before pulling out his gun. An investigation was also launched this week after a man suffered burns in the back of a police van.
This week a French police officer was cleared of responsibility over the death of an environmental activist killed by a stun grenade during a 2014 protest.
In 2016 there were protests after a young man Adam Traoré died in police custody and French police sparked riots last year around Paris after a youth had a police baton inserted in his anus as he was arrested.