Pictures on social media showed the car in flames while parked in the middle of the road on the Quai de Valmy, by the Canal Saint Martin in north eastern Paris.
It remains unknown exactly who lit the fire, but a journalist at Le Monde tweeted that three police officers had "abandoned" the car after it was descended on by rioters. The same reporter wrote that a Molotov cocktail had been thrown through the car's back window.
Firefighters were quick to extinguish the blaze, and there have been no reports of injuries.
The road has since been completely shut down, reported The Local's Hattie Ditton from the scene, as nearby residents watch the commotion from their windows.
"Police are trying to get everyone out of the way, but onlookers are saying that the counter-protesters are now demonstrating due to the police's protests at the Place de la République," she said.
The Place de la République, a huge public square nearby, has meanwhile been cordoned off by police who have taken the area for their own protests.
Many people were on hand protesting against the police, with some questioning why police were allowed to use force during the protests.
"We are humans too, why is there one rule for them and another for us," one told The Local.
Photo: Hattie Ditton/The Local
A violent minority of labour law protesters are part of the reason why police are protesting on Wednesday, with police unions calling for the protest after 350 officers have been injured so far by the protesters.
Officers are understood to be protesting in 60 areas around the country.
Despite the clashes, 82 percent of the French have a positive opinion of the police, according to an Odoxa survey.
Philippe Lavenu, from leading police union Alliance, said that officers were fed up with the "anti-cop hatred", which shows a marked difference from when crowds would cheer the police after the January terror attacks last year.
"We have gone from being embraced by the crowds after the Charlie Hebdo killings to being attacked repeatedly in the streets," he told The Local earlier this month.
“We are exhausted. We are sick of this and that's why we are calling on officers to protest," added Lavenu. “We don't deserve it. We had an incredibly tough year in 2015 with the two terror attacks. Officers have been working on their days off and without holidays and they are worn out."
Additional reporting by Hattie Ditton