Critics of the restrictive measures say they are excessive and primarily affect children and the poor.
Protesters clashed with police in several places in the capital. Police fired tear gas at the Champs-Élysées. In Marseille, protesters turned against a camera crew from television channel BFMTV and a journalist is said to have been kicked.
Last week, at least 110,000 people demonstrated against the restrictions imposed by the government in the interests of public health. Almost as many were expected on Saturday.
The measures were tightened last week. Visitors to French museums, cinemas and event venues have been required to show proof since Wednesday that they have been vaccinated against the coronavirus or tested negative. The government plans to tighten the rules even further in August. Then people also have to show such a vaccination certificate in catering establishments and some shopping centers.
There is a lot of resistance among the French, including in business such as the catering industry. Cinema owners have complained that they have seen their clientele drop by 70 percent since Wednesday. An association of restaurants has announced that it will not review the requirements.