French President Emmanuel Macron has called for "calm and order" and warned riots across the country must not escalate, during a national television address.

Speaking from the Élysée Palace in Paris, the president said "we all feel anger and shame" after a major day of protests turned into rioting and looting across France on Saturday.

Some 550,000 demonstrators took to the streets for largely peaceful protests against rising fuel prices, the cost of living and deteriorating public services, including schools.

Macron urged a distinction between the "legitimate demands" of protesters and "those who destroyed, smashed and looted". Police have arrested about 2,400 people.

France's president said "nothing justifies" the "unbridled" violence seen and said those involved would face justice.

Groups of rioters, some dressed in black and wearing masks and balaclavas, also came out in Paris, Marseille and other towns and cities, with some setting fire to cars and buildings.

Widespread looting took place across the cities of Paris, Marseille and Lille, as well as other areas.

Macron said local prefects and mayors will work together across the country to do what they need to do to protect shops and buildings.

Macron also said there would be "full transparency" over the police response to the demonstrations.

Tear gas and water cannon were turned on crowds over the weekend and riot police were seen hitting people with batons in several places.

France's interior ministry said about 1,000 police officers were injured on Saturday, seven of them seriously.