French President Emmanuel Macron has urged people to remain calm and maintain order following widespread protests across the country, as tensions continued at several locations in Paris on Sunday, a day after violent clashes and looting.

Addressing the nation from the Élysée Palace, Macron warned those involved in violence during the demonstrations against escalating the situation further.“We all feel anger and shame,” he said, according to a BBC.

The French government said around 550,000 people had taken part in nationwide demonstrations against rising fuel prices, inflation and deteriorating public services, including schools. Most of the protests remained peaceful.

Macron said it was important to distinguish between protesters with “legitimate demands” and those involved in vandalism, rioting and looting.According to France’s Interior Ministry, around 2,400 people have been arrested.

The French president said there could be no justification for uncontrolled violence and those responsible would be brought to justice.In Paris, Marseille and other cities, some people dressed in black and wearing masks were involved in unrest, while vehicles and buildings were set on fire in several locations.

Violence erupted during nationwide protests on Saturday against inflation and problems affecting schools.The French government said at least 550,000 people had taken to the streets amid what it described as an “escalation of violence”.By the evening, tensions between riot police and demonstrators had intensified in Paris, where officers used tear gas and water cannon to disperse crowds.

Several buildings were set on fire in the capital and elsewhere. In Limoges, a major fire at the town hall caused part of the building’s roof to collapse.Looting was also reported in several cities, with town halls and commercial premises suffering extensive damage.Prime Minister Sébastien Lecornu said 150 police officers had been injured during the unrest.

The main march held in the French capital in the afternoon was largely peaceful. A group of young people told the BBC they were “peaceful” and were “just trying to change things, but nothing is changing”.

However, as the day progressed, some groups set fires in the streets and torched several vehicles. Incidents were also reported around Paris’s famous Place de la République and other locations.Shops were vandalised and looted, while at least one restaurant was completely destroyed by fire. The BBC also witnessed clashes between different groups.

In central Paris, riot police were seen advancing towards crowds and striking some individuals with batons.In Lyon, Mayor Grégory Doucet described the arson attack on the city’s tourist office as a “tragedy”.Speaking to BFM TV, he said: “We are heartbroken by this incident because it is a very well-known historic building.”

Local police said “anti-social elements” had also prevented firefighters from safely tackling blazes.Fire crews attempted to bring the fire at Limoges town hall under control, where part of the building had collapsed, according to local authorities.

Régis Juanico, the mayor of Saint-Étienne, said on social media that a young man had lost his hand when a small explosive device detonated in the city.He said: “Such a tragedy should never have happened.”

Over the past few weeks, hundreds of students have staged protests at France’s lycées secondary schools for pupils aged 15 to 18 — over teacher shortages and deteriorating facilities.The demonstrations subsequently grew significantly as trade union members and other protest groups joined the movement.These included the so-called Yellow Vests (Gilets jaunes), a movement that staged more than a year of protests against rising living costs from 2018, becoming one of France’s longest-running protest movements.

France’s Interior Ministry said Saturday’s demonstrations had seen incidents of “organised violence” involving masked individuals in cities including Paris, Marseille, Rennes, Toulouse and Angers.Reports of damage to buildings also emerged from cities across France, including Grenoble, Avignon, Pau, Montpellier and Valence.

In Paris, clothing and grocery shops were looted, while an Apple Store in the northern city of Lille was vandalised and subsequently evacuated.A video verified by BBC Verify appeared to show several masked individuals driving a tourist train through a narrow street in Grenoble towards at least three riot police officers.

Although protests and unrest are not unusual in France, the latest developments come at a time of growing political uncertainty in the country.

Macron is due to leave office next year, while opinion polls suggest that the presidential election in April could see a closely fought contest involving Marine Le Pen, leader of the National Rally, and Jean-Luc Mélenchon, leader of the hard-left party La France Insoumise.

Mélenchon later joined the demonstrations and accused police of using “violence” against protesters, although he also condemned looting and arson.Prime Minister Lecornu described Mélenchon’s remarks as “dangerous and reprehensible”.

Lecornu had earlier said police had faced “extreme violence” and suggested that some groups were using the demonstrations as a “warm-up” for the next presidential election.

“No one can impose their political agenda through violence,” he added.

Meanwhile, Le Pen said protesters’ “legitimate demands” had been “held hostage by left-wing groups”. She also accused Mélenchon of inciting violence.Macron said: “Those who vandalised property, attacked public offices and commercial premises, and targeted our town halls will be prosecuted and punished.”

The government has also announced measures aimed at addressing some of the grievances behind the protests.Education Minister Édouard Geffray promised to recruit an additional 3,000 teachers during a television interview on 8 October.However, despite these announcements, demonstrations continued and intensified as the days went by.

Who are the protesters?

BBC News spoke to several demonstrators on the streets of Paris.One student said taking part in the protests was “very important”. They said students were not the only people on the streets, with workers and other employees also joining the demonstrations.

After weeks of student protests, the so-called Yellow Vest movement and trade unions have joined young people in broader demonstrations against rising living costs and the deteriorating state of public services.Another student told the BBC that “all generations” were out on the streets to protest against these problems.

“This gives us real strength to move forward and make our voices heard by the government,” they added.Another demonstrator said they were “fighting against the rise of extremist politics”.Commenting on the current situation, they said: “It has become impossible to live under these conditions.”