About 400 people were arrested nationwide, Interior Minister Laurent Nuñez said.
Nuñez said 110 marches drew about 550,000 people across the country. Organisers, including the CGT labour union and students' organisations, said about 800,000 demonstrators took to the streets.
Nuñez described troublemakers as "extremely violent, radical far-left groups" whom, he said, sought confrontations with police and targeted public buildings, including city halls and local government offices. He said those groups have been joined by offenders willing to loot shops. Most of those arrested are adults, he said.
"There is no place for violence in our Republic," French President Emmanuel Macron said in a message on X. "Those who vandalized property, attacked government offices and businesses, and even looted our town halls will be prosecuted and punished."
"We will stand united against those who sow chaos … and who prevent people from peacefully expressing their demands," Macron added.
Police in Paris fired tear gas and water cannons to push back people wearing hoods and masks and throwing fireworks, paving stones and other objects at officers in the Place de la République.
Many metro stations were closed on Saturday.
The majority of peaceful protesters joined a march that moved toward northwestern Paris. The crowd chanted France's national anthem and waved flags, and some people played trumpets and violins.
In the southern port city of Marseille, some shops and a municipal police station were damaged, while protesters briefly forced their way into the lobby of City Hall.
Nuñez also reported violence by masked groups against local government buildings in Bordeaux, break-in attempts at Lille and Calais city halls and at a police station in Brest. Violence also broke out in Rennes, Toulouse, Montpellier and Grenoble, among other cities.
In Limoges, a middle-sized town in central France, the City Hall was set on fire. Flames were still raging Saturday evening.
Protesters responded to calls on social media to revive the "yellow vest" movement, which emerged in 2018 against social injustice. Demonstrators expressed widespread frustration and anger at the government as gasoline, energy and food prices have spiked in recent months.
Many protesters could be seen wearing the fluorescent yellow vests that became a symbol of the 2018 rallies.
Student groups protesting since mid-September through school blockades have urged supporters to join them.
The CGT, one of France's major labour unions, also backed the protests, calling for "higher wages and pensions, lower prices and the protection of public services that meet people's needs."
Authorities opened an investigation after a young protester was badly injured Saturday and lost a hand in Saint-Etienne, Nuñez said. He declined to confirm French media reports the injury was caused by a police grenade explosion.
The incident comes as the police have drawn sharp scrutiny over their use of grenades and other riot-control weapons during recent demonstrations.
In the past weeks, France has seen thousands of arrests, hundreds of injuries and schools set on fire as the new school year descended into nationwide student protests that are influencing the country's presidential election campaign and drawing international attention.
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