In a video of the incident, we see dozens of “yellow vest” protesters throwing stones and other objects at three police officers.
One of the policemen kicks a protester while a man dressed all in black knocks over one of the officer's motorbikes.
As the violence increases, one of the officers pulls out his gun.
Eventually the police officers escape, with two of them on the same bike, while the third motorbike remains on the ground.
The three officers were blocking one of the roads leading to the Champs-Elysees in the 8th arrondissement of Paris where about 2,000 yellow vests were marching when they became a target.
The incident took place at about 5.30 pm on Saturday after a day of mostly calm “yellow vest” protests in the French capital and elsewhere across France.
The violence was captured on video by a journalist who was present at the scene and the images quickly went viral.
Overall fewer French “yellow vests” turned out for a sixth Saturday of protests, targeting border points as fatal road accident brought the death toll to 10 since the movement began last month.
A total of 38,600 people took part in protests across the country, well down from the 66,000 by the same time the previous Saturday, the interior ministry said. There were 220 people detained nationwide, 81 of whom were taken into police custody, it added.
The number of demonstrators has been trending downwards since 282,000 people turned out for the first Saturday protest against planned fuel tax hikes on November 17.
The movement, characterised by the high-visibility yellow vests worn by the protesters, then morphed into a widespread demonstration against French President Emmanuel Macron's policies and style of governing.
Health minister Agnes Buzyn told Le Journal du Dimanche (The Sunday Newspaper) Macron's government was “in step with the demands of the yellow vests” as she called for “a more constructive dialogue”.
Prime minister Edouard Philippe told the same newspaper his relationship with Macron has only “intensified” during the crisis, rather than become strained, as has been reported.
“We talk a lot. We tell each other things,” he said.