A man has been arrested after a fire at the town hall of Limoges, according to French media.
The man was arrested early in the morning in Val-d'Issoire, Haute-Vienne, BFM reports.
He is 34 and authorities consider him a member of the ultra-left, according to a source close to the case.
Justice minister Gerald Darmanin said the person was being held in police custody and may not have acted alone.
Overnight curfews helped keep the calm, French PM says
On Saturday, flames engulfed the 19th-century city hall, causing the roof to collapse and the building's clock tower to fall in striking images broadcast worldwide.
In France, demonstrations that started over deteriorating school facilities in Paris' northern suburbs morphed into some of the country's worst unrest in decades.
One protester died on Saturday after suffering a cardiac arrest during protests in the capital.
On Sunday evening, small groups set rubbish bins, bicycles and other objects on fire in the streets and looted businesses in Paris, Lyon, Marseille and other cities.
Mr Darmanin told the French TV network BFM that 149 people held at the weekend were in detention awaiting trial. He added about 2,500 were still in custody for questioning.
Nearly 1,000 officers were injured, French interior minister Laurent Nunez said.
French President Emmanuel Macron voiced the public's "anger" and "shame" on Sunday over rioting and looting during nationwide protests against rising living costs and poor conditions in schools.
The government said on Tuesday France will reinforce police with troops and mount a huge security operation for more protests planned on Saturday.
"The deployment next Saturday will be massive," Prime Minister Sebastien Lecornu said.
Overnight curfews in violence-hit zones of French cities helped bring some calm after the nation's worst unrest in years, ahead of more demonstrations planned for the weekend, the government said.
The government tried to reassure the public it had learned from security oversights that left the centres of cities such as Paris, Marseille and Lyon largely unprotected from rioters and looters moving in after protests.
Mr Lecornu said restrictions may be extended further into the week if the unrest continues.
Parliament is also setting up a commission of inquiry to establish the causes of the unrest, while 200 investigators have been assigned to identify and track down those involved in the street violence.
Framing the crisis as a choice "between violence and the Republic", Mr Lecornu blamed the disorder on far-left groups, who in turn have accused the government of underestimating public anger over high living costs and declining public services.
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Mr Lecornu invited political parties from both his government and the opposition to hold consultations on Thursday.
Marine Le Pen's far-right National Rally said it would send a representative.
Over the weekend, crowds also took to the streets in other countries, including Italy, Portugal and Albania, where there has been similar anger over living conditions.
In Milan, police clashed on Sunday with demonstrators hurling stones and looting stores during protests over poor public services and rising living costs.
On Tuesday, Italian Prime Minister Giorgia Meloni approved a raft of security measures, including a new offence of violent participation in a protest, stricter penalties for rioters, and financial liability for parents whose children take part in vandalism and looting.
The government said it would deploy 500 army troops alongside the police in Milan until the end of 2026.
(c) Sky News 2026: Suspect arrested in France after fire at Limoges city hall
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