Thousands demonstrated in cities across France on Saturday against tighter restrictions on people not vaccinated against COVID-19, as parliamentary wrangling continued over the draft law.

In the capital Paris, the largest single gathering set off from near the Eiffel Tower, called by fringe anti-EU presidential candidate Florian Philippot.

Other demonstrations harked back to the 2018-19 "yellow jackets" protests against President Emmanuel Macron's perceived favouring of the wealthy, while there were further gatherings in major cities like Bordeaux, Toulouse and Lille.

People in the crowd chanted "no to the vaccine" or "freedom for Djokovic", seizing on the case of world tennis number one Novak Djokovic, who is fighting the Australian government to compete unvaccinated in next week's Grand Slam Australian Open.

"Novak is kind of our standard-bearer at the moment," demonstrator Pascal told AFP in Bordeaux.

He was marching alongside parents with children at a tennis club in the western city, where he said the coach risks losing his job for refusing vaccination.

In Paris, demonstrators bore French and regional flags, with banners bearing messages like "it's not the virus they want to control, it's you".

"It's Nazism, it's apartheid, I haven't been jabbed and I'm against vaccines in general," 60-something demonstrator Claire said.

Two others, Laurence and Claire, told AFP they were vaccinated "but we're against the pass for teenagers, we don't see why they're being vaccinated because they aren't in danger".

While officials had not published an estimate of nationwide turnout by late afternoon, police or local authorities counted around 1,000 each in Lyon, Nantes, Bordeaux and Marseille.

Demonstrators were hoping to outstrip the 105,000 who hit the streets last weekend -- some possibly mobilized by Macron's declaration in a newspaper interview that he wanted to "piss off" the unvaccinated with new restrictions until they accepted a coronavirus shot.