A suspect linked to a far-left movement has been arrested in France after a 19th Century city hall was gutted by a fire over the weekend that broke out during mass disorder, French media report.

The clock tower and parts of the roof of the ornate city hall in the central city of Limoges were engulfed in flames before collapsing on Saturday.

The 34-year-old suspect is known to police for acts of violence against public officials and is on a French national security watchlist, FranceInfo and BFM TV report.

French Prime Minister Sébastien Lecornu has vowed a "massive" police presence during further protests planned for Saturday, while several cities, including parts of Paris, will be subject to curfews this week.

Marseille mayor Benoît Payan said on X that the prefect had decided to introduce the curfew "starting this evening and for days to come", with French media reporting it would be in place overnight from Tuesday to Friday.

Payan said the measures apply to minors and will only be in commercial areas of the city, which were particularly affected by looting which took place last weekend.

Paris's police commissioner has also ordered the extension of an overnight curfew in the capital. The Préfecture de Police said the measure would continue "for as long as it proves necessary".

A curfew for parts of central Lyon was renewed on Tuesday, while overnight curfews for Nice and Lille are ongoing, and a week-long, overnight curfew for Bordeaux came into force on Tuesday night.

French Justice Minister Gérald Darmanin told BFM Television that 149 people were in detention following widespread demonstrations over the weekend.

Hundreds of thousands of demonstrators took to the streets to protest against rising fuel prices, the cost of living and deteriorating public services, including schools.

Darmanin previously said he asked prosecutors to be "extremely firm" and "ruthless towards those who attacked police officers, gendarmes and firefighters, who looted shops and who attacked public buildings".

Lecornu told French parliament on Tuesday afternoon a large number of police would meet demonstrators at a planned protest on Saturday.

Interior Minister Laurent Nuñez previously admitted police had "lost control" in some cities over the weekend.

He was strongly criticised by opposition politicians over authorities' preparedness for the disorder, leading him to offer his resignation on Monday, which was rejected by President Emmanuel Macron.

Lecornu also accused far-left groups of an "insurrectionary" plan over the weekend's mass chaos.

Responding to an earlier, similar accusation from Lecornu, left-wing La France Insoumise (LFI) de facto leader Jean-Luc Mélenchon had called for the prime minister to "prove his accusation" or "apologise, shut up, and stop stoking disorder".

On Tuesday, Mélenchon urged followers on social media to show "restraint" in the face of any "provocation".

Lecornu earlier said targeted curfews introduced across France on Monday contributed to a quiet night following the disorder.

Curfews were introduced across parts of central Paris, including Place de la République, where protesters had gathered over the weekend, and the Les Halles shopping area.

Other measures restricting the movement of young people and gatherings were introduced on Monday in cities such as Marseille, Bordeaux, Nice and Lyon in the south, as well as Lille and other towns in the north.

A crowd assembled in Lyon on Monday night in support of businesses affected by the disorder but dispersed without violating the curfew, officials said.

The Rhône prefecture said on social media that it was "furious" that a far-right group tried to hijack the gathering. The prefecture said on X it reported the group to the public prosecutor for alleged Islamophobic and xenophobic remarks.

Lecornu thanked police officers and gendarmes for enforcing the measures, adding that further curfews on Tuesday night would be decided depending on where they were necessary.

More than 2,500 people have been arrested since the disorder broke out, officials said on Monday. One demonstrator's hand was blown off by a police crowd-control grenade, according to the AFP news agency. About 1,000 police officers were injured.

Protests first began last month with students demanding better school conditions but they have escalated to take in a broader range of concerns with numbers at demonstrations bolstered by trade unions and various protest groups.

More than 2,000 shops and other businesses have been directly impacted by the weekend's violence, the head of France's Chambers of Commerce and Industry (CCI) said.

Rioters, some dressed in black and wearing masks and balaclavas, were seen setting fire to cars and buildings and looting businesses in Paris, Marseille and other cities and smaller towns.

Protest organisers earlier declared that a second round of protests will take place on Saturday across France.

The so-called yellow vests (gilets jaunes), who were responsible for France's longest-ever modern protests in 2018, has said "Act II" will take place this weekend.

Meanwhile, French union La CGT has called for a major day of strikes on 5 November.