France's Prime Minister Sébastien Lecornu is holding a crisis cabinet meeting on Monday to assess a weekend of violence and looting across the country, in what were some of the worst scenes of public disorder in modern French history.

On Saturday over half a million mainly peaceful protesters demonstrated against rising living costs and dwindling access to decent public services, including a good state education. But the protests turned nasty after groups of black-clad, masked activists and vandals appeared.

An estimated 1,500 shops and businesses were looted and destroyed. Riot police fired tear gas and turned water cannon on crowds. They 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.

There had been rumours in France that President Emmanuel Macron may introduce a temporary curfew in parts of the country, or even impose a state of emergency to help calm the febrile atmosphere. In the end, he used a televised address to the nation on Sunday to call for national unity and to try to assure the French public that the perpetrators of the violence would be punished.

Macron's speech has been roundly criticised on social media forums and by political opponents for lacking concrete detail.

How will vandals and rioters now be brought to account?

How might France's towns and cities be better protected - especially since new mass demonstrations have been announced in a couple of weeks' time?

Exactly how will destroyed businesses be compensated?

And when will a dialogue be established with students and teachers' bodies on the subject of education?

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On Sunday the Secretary General of the CGT union, Sophie Binet, accused Macron of failing to address students' concerns, the cost-of-living crisis or the dwindling quality of public services in France.

He's apparently passed that baton to Prime Minister Lecornu. Yet he and his interior minister are charged by many in France with being woefully ill-prepared and under-policed ahead of Saturday's multiple, scheduled protests.

The president of France's lower house of parliament, Yaël Braun-Pivet, says she wants to open an inquiry into exactly what happened this weekend and why.

"Things are dark in the city of light [a nickname for Paris]" was the graffiti I read daubed in red paint across a wall adjacent to a row of shattered shops in the French capital on Sunday night.

Macron is widely viewed here as a lame-duck president. He is on his way out. There's a hotly contested race under way to become his successor, with the vote scheduled in six months' time. The presidential candidate from the anti-immigration nationalist right (Marine Le Pen) and also the anti-capitalist left (Jean-Luc Melenchon) are vying to make headlines.

That is adding to current tensions in France - in politics as well as on the streets.

Parliament here is paralysed, deeply divided between three vying political blocks.

Then there are France's financial woes too. Investors are leaning hard on this country to get its spiralling public debt under control. But the French government worries, if it cuts public services or welfare, yet more angry people will pour out onto the streets.

What now, what next, is our country broken? You hear these questions a lot at the moment.

People across France were shocked and troubled by Saturday's events. The images of tear-gassed towns, apparently unimpeded looters and burning public buildings have worried the nation.

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Many passers-by I speak to express frustration that, while they worry about the future, their leading politicians seem, instead, to be passionately focused on finger-pointing; blaming one another for the volatility.

"While we worry for our safety, they use this situation as a pre-presidential election political football," teacher and father of three Edouard told me.

Macron and his prime minister blamed Saturday's violent chaos on radical far left groups and delinquents; hard left leader Jean-Luc Melenchon alleged government "incompetence"; Marine Le Pen on the nationalist right, which likes to be seen as strong on law and order, posted a video seated in front of the French flag, giving a presidential-style address blaming the "Macronist administration that is out of steam, exhausted, and disoriented".

For the next two weeks, the French authorities hope for a bit of a respite. Students start their half-term break as of Monday.

But on 5 November, a cross-section of trade unions, plus France's disparate "yellow jacket" (gilets jaunes) movement that staged demonstrations for over a year in 2018 - during Macron's first term as president - have announced huge protests.

France is holding its breath.