The French interior ministry said 118 people had been injured in the protests in several cities, including 17 law enforcement officers.
More than 500 people have been taken into custody.
The "yellow vest" movement opposed fuel tax rises but ministers say it has been hijacked by "ultra-violent" protesters.
An estimated 125,000 demonstrators gathered across the country during the day, with 10,000 of them in the capital, where the scenes were the most destructive.
In a television address on Saturday evening, Prime Minister Edouard Philippe said the "casseurs" (troublemakers) were still at work.
He called for more communication between the government and protesters to resolve the conflict. "The dialogue has begun," he said. "It is now necessary to rebuild the national unity."
What is happening this weekend?
Apart from Paris, there were demonstrations in several other cities on Saturday including Lyon, Bordeaux, Toulouse, Marseille and Grenoble.
Protests against climate change have also been held place in Paris and other cities.
There have been a number of confrontations in the capital. Some protesters have been seen smashing shop fronts, setting fire to cars and painting walls with graffiti.
Video footage showed one demonstrator being hit in the torso with a rubber bullet while standing in front of a line of police with his hands up. At least three members of the press were also hit.
Water cannon were deployed on a street east of the city centre.
As night fell, protesters converged on Place de la République, and a heavy police presence remained on the Champs-Elysées
.
Nearly 90,000 officers were deployed countrywide in anticipation of clashes, including 8,000 in Paris where 12 armoured vehicles were also utilised.
Mr Philippe praised the interior ministry and police for putting together a plan to ensure the damage was not as bad as the previous weekend.
Last week, hundreds of people were arrested and 162 were injured in violence in Paris - some of the worst street clashes in the French capital for decades.
This weekend, six matches in the top tier of France's football league were postponed. The Louvre, Musée d'Orsay and other sites were also closed all day in Paris.
The vandals move in
By Hugh Schofield, BBC News, Paris
As evening descended, the focus shifted away from the Champs-Elysées to the surrounding streets and boulevards.
This is where the genuine yellow-vest protesters were outnumbered by groups of political agitators and common vandals.
They torched cars and smashed shop windows, much as they did last week.
The riot police reacted swiftly - charging rioters and sending in snatch squads to seize suspects. It was a scene of sporadic violence, but compared to last Saturday, the forces of law and order appeared to be more in control.
How have the protests spread?
The sentiment of the anti-government protests has inspired other spin-off protests in nearby countries. About 100 people were arrested in the capital Brussels. Some threw paving stones, fireworks, flares and other objects at police, according to AP news agency.
In the Netherlands, a protest was held outside parliament in The Hague, with an estimated 100 participants.
Where are we with the yellow vest movement?
The "gilets jaunes" protesters are so-called because they have taken to the streets wearing the high-visibility yellow clothing that is required to be carried in every vehicle by French law.
The BBC's Lucy Williamson in Paris says that over the past few weeks, the social media movement has morphed from a protest over fuel prices to a leaderless spectrum of interest groups and differing demands.
Its core aim, to highlight the economic frustration and political distrust of poorer working families, still has widespread support, our correspondent says. An opinion poll on Friday showed a dip in
support for the protests, but it still stood at 66%.
President Emmanuel Macron's ratings have fallen amid the crisis, and he is planning a national address next week, his office has said. Some have criticised him for keeping too low a profile.
What has the government conceded?
The government has said it is scrapping the unpopular fuel tax increases in its budget and has frozen electricity and gas prices for 2019.
The problem is that protests have erupted over other issues.
Granting concessions in some areas may not placate all the protesters, some of whom are calling for higher wages, lower taxes, better pensions, easier university requirements and even the resignation of the president.
Some of Mr Macron's critics call him "the president of the rich".
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