The interior ministry said 272 people had been arrested by mid-afternoon after violent incidents involving hooded individuals, including in Paris, Marseille in the south, Rennes in the northwest, Toulouse in the southwest and Angers in the west.
"Such actions include attempted looting, confrontations with law enforcement, the setting of fires to street furniture and the targeting of seats of power and media outlets," it said, blaming the unrest on what it described as the "ultra-left".
In Lyon, in east-central France, protesters also set ablaze a tourist office.
The protests began last month at high schools in Paris' poor northern suburbs, where anger over teacher shortages and shabby facilities evolved into a broader movement focused on inequality, public spending and living standards.
"We are fighting because the cost of living is too harsh, because the price of fuel is too high, because high school pupils are being violently attacked and hurt all over the country just for trying to protest and ask for more teachers and decent learning conditions," said Lola, a 19-year-old protester in Paris.
Protesters in high-visibility vests blocked streets, recalling the Yellow Vest movement that marked President Emmanuel Macron's previous term in office.
In the French capital, police used tear gas and water cannons to push back people wearing hoods and masks and throwing fireworks and other objects at officers in the Place de la République, northeast of the Paris city centre.
Large numbers of riot police were deployed in the square and surrounding streets.
The majority of peaceful protesters joined a march that moved toward northwestern Paris.
The crowd chanted France's national anthem as French flags were waved.
The chants were accompanied by people playing trumpets and violins.
Police were working to prevent other small groups of protesters from converging on government buildings, the interior ministry said.
In Marseille, the mayor said the town hall had been vandalised and that additional police were being sent to the city following talks with the prime minister and interior minister.
About 100 people walked towards the start of the protests shouting "All cops are bastards," according to a Reuters witness.
Macron, who urged calm on Friday, is entering the final stretch of his presidency amid a fragmented political landscape and growing pressure over the economy.
France's efforts to reduce public debt have failed to reassure investors, pushing government borrowing costs to their highest levels in more than two decades.
Police tactics have drawn criticism following a series of injuries among demonstrators, including a teenager who lost a hand after picking up a stun grenade.
Prime Minister Sebastien Lecornu said more than 900 police officers had also been injured in previous protests.
The police watchdog is investigating at least two dozen allegations of police violence.
France suspended the use of stun grenades during the student demonstrations but Interior Minister Laurent Nunez said they could be used on Saturday.
Calls on social media for veterans of previous protest movements to join the demonstrations appeared to have broadened participation, raising the prospect of larger protests.
The yellow vest movement emerged in 2018 in opposition to diesel taxes before expanding into a wider protest against living costs and inequality.
The movement subsided after Macron announced billions of euros in tax cuts.
Yannick Maillou, a teacher from La Crèche in western France who participated in the yellow vest movement, said several gathering points had been organised locally for Saturday's protests, with labour unions also encouraging participation.
with DPA and AP
