Organisers claim their goal is to peacefully voice opposition to infringement on their "freedom" and "fundamental rights".
But authorities claim the movement's objective is to "block the capital" and banned a planned demonstration in Paris.
The truckers' protests that inspired France's movement have paralyzed Ottawa, Canada's capital, and forced authorities there to declare a state of emergency. As of Friday morning, more than 350,000 users had joined a Facebook group connected to the movement.
On Wednesday several convoys left Nice, Bayonne and Perpignan in the south, aiming to reach the capital by Friday night. There have been calls to join Brussels for a "European convergence" scheduled for Monday.
About 200 people gathered in a parking lot in Nice with posters and French and Canadian flags, Reuters reported. Not all of the people setting out from Nice planned to travel all the way to Paris or Brussels. The convoy was made up of motorcycles and private cars, but no trucks.
“Our work is to communicate to Europe that putting in place a health pass until 2023 is something the majority of our fellow citizens cannot understand,” a man named Denis told Reuters.
By Friday morning, drivers had already left the northern city of Lille for Paris, a 225-kilometre drive.
A large crowd in the eastern French city of Strasbourg gathered Friday morning to prepare for the journey as well.
Another convoy left Lyon, in central France, Friday morning. Photos showed a smaller group gathered on an overcast morning, waving French flags and preparing for the journey in a parking lot.