Some 136,000 demonstrators, a lot of them peaceful, were counted across the country on Saturday, the interior ministry said Sunday.
Fringe groups from the far-right and far-left have infiltrated some actions, including Saturday's protests in Paris, authorities say.
The violence in Paris was the worst in the elegant centre of the capital since the May 1968 student uprising that brought France to its knees.
Opposition parties criticized the government for allowing violence in demonstrations and trying to undermine the legitimacy of protesters.
But the protests have evolved into a broader demonstration against French President Emmanuel Macron, his government and tensions between the metropolitan elite and rural poor. "They betray the causes that they pretend to serve and which they manipulate", Macron said on Saturday. The president visited some of the flashpoint locations on Sunday.
Demonstrators claim that they've finally had their fill of Macron's overbearing nanny state, and that a recently introduced package of taxes and regulations meant to curb fossil fuel consumption by dramatically increasing the price of gasoline were the last straw in their dissatisfaction with Macron's government.
One of the country's most famous monuments had been set upon by a violent wing of the "gilets jaunes" (yellow vests) protest movement, and beneath the smashed statue of Marianne - a symbol of the Republic - the anti-Macron graffiti would have been impossible to ignore.
Mr Macron, in office for just 18 months, is the chief target of their anger. He was asked why thousands of French police couldn't prevent the damage, especially to the Arc de Triomphe.
Three people have been killed in relation to the protests since November 17.
Then later Saturday younger delinquents appeared, in particular near the Place de la Bastille and on the edges of the Champs-Elysees avenue, where news agency AFP journalists watched them looting a small supermarket and burning a scooter.
The far-right leader Marine Le Pen blamed the extreme left, but ministers and observers of social conflict pointed to the involvement of far-right activists.
But the vast plumes of smoke and tear gas that clouded the capital on Saturday were a testament to the escalation of violence in Paris.
Access to the avenue was closed to cars and strictly monitored by police with identity checks and bag inspections.
Michel Delpuech, the chief of police in Paris, said Sunday that fires were started at six buildings and more than 130 makeshift barricades and 112 vehicles were torched. Firefighters came under attack and one demonstrator was hurt when struck by iron railings that were toppled over in the Tuileries gardens neighbouring the Louvre.
Almost 190 fires were put out and six buildings were set alight, the interior ministry said.
Some demonstrators removed the barriers protecting the Tomb of the Unknown Soldier from World War I under the Arc de Triomphe monument to pose near its eternal flame and sing the national anthem.
Paris Mayor Anne Hidalgo said in a post on Twitter she was "indignant" about the violence, and said "our country is faced with a profound crisis which can only be resolved by dialogue".
Referring to the possibility of imposing a state of emergency - a demand made by the police union Alliance - Castaner declared: "Nothing is taboo for me".