French President Emmanuel Macron has called for "calm and order" after a major day of protests turned into rioting and looting on Saturday, and as some disorder continued in Paris on Sunday.

In a national address from the Élysée Palace, he warned those who had taken part not to "escalate", adding: "We all feel anger and shame."

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 said a distinction must be drawn between the "legitimate demands" of protesters and "those who destroyed, smashed and looted".

Police have arrested about 2,400 people, according to France's interior ministry.

The French 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.

On Sunday, looting and clashes with police continued on a smaller scale in parts of the capital and Lyon.

Tear gas and stun grenades were fired at hundreds of people in Paris, according to the AFP news agency, and bottles and rocks were again hurled at police.