PARIS — Hundreds of thousands of protesters inspired by frustrated high school students took to the streets across France on Saturday in a third consecutive weekend of demonstrations over living costs and education.

Youth-led protests were also held elsewhere in Europe, including in Germany and Portugal.

France’s protests were overwhelmingly peaceful, with whimsical Halloween costumes lightening the mood, but gatherings in Paris and other cities ended in clouds of tear gas and scattered fires set by small groups on the margins.

About 70,000 police and gendarmes were deployed across the country after French Interior Minister Laurent Nuñez warned of a “very high risk” of disorder, especially after dark on Halloween. Paris marches were rerouted to the capital’s edge to protect stores, government buildings and touristed areas in the city center.

France’s government estimated that 320,000 people protested nationwide Saturday, fewer than in previous protests but still a significant turnout. Mass protests on Oct. 17 that deteriorated into some of France’s worst rioting in years drew 550,000 people around France, and demonstrations on Oct. 24 drew 410,000, according to government estimates. Organizers’ turnout estimates are higher.

Authorities in France reported more than 560 arrests nationwide by Saturday night. Police had arrested thousands of people following riots and looting that marred marches the previous two Saturdays.

In the main Paris march, each group carried its own banner: high school students, climate activists and people angry about the cost of living.

Corentin Cabreux, a 21-year-old student, said that he lives in a state-run student residence where “there are damp stains all along the bottom of my walls, whole sections peeling off, cockroaches everywhere, rats.”

An information technology worker protested in solidarity with the students and her mother, who was struggling with a minimum wage job. A gray-haired woman carried a sign reading ‘’The Old are Fed Up Too.”

Halloween costumes reflected the mood. Cléo Farenc, a 30-year-old gallery assistant, came dressed as a beheaded Marie-Antoinette.

“It’s about embodying a figure of power who was brought down by the people,” she said. “It’s a very strong symbol in French culture.”

The rallies in France were started last month by high school students protesting neglected buildings, teacher shortages and a university admissions system seen as unfair to disadvantaged students. Labor unions and others angry at the leadership of President Emmanuel Macron joined in with a variety of demands.

On Saturday, the crowd streamed along the Boulevards des Maréchaux, avenues that ring the edge of Paris, in a march that was joyful for hours. Techno music blasted from speakers, and some marchers went trick-or-treating. A police helicopter hovered overhead as the sun set slowly over the city.

Later, clashes broke out near Porte de Charenton, where the march ended. Protesters hurled glass bottles and fireworks at police. Officers responded with volleys of stun grenades and tear gas. The blasts echoed through the streets, and smoke filled the air as dusk fell.

Many peaceful marchers turned back, coughing, their eyes streaming with tears, and left the march, some scattering into the nearby Bois de Vincennes, one of the largest parks in Paris.

While the vast majority of protesters have been peaceful, groups of troublemakers routinely target police with fireworks and projectiles. Police use tear gas, dispersion grenades, water cannons and other tactics that have resulted in severe injuries.

Paris police barred people from entering Place de la Republique and Les Halles — neighborhoods popular among young people — from 11 p.m. to 6 a.m. Saturday and Sunday.

Unaccompanied minors face a separate 9 p.m. curfew around the Champs-Elysees. A Paris court on Wednesday suspended an earlier curfew on minors as a serious and illegal infringement of freedom of movement.

In Germany, a youth initiative called “Gen Z regelt” — roughly “Gen Z’s got this” — rallied in more than 30 cities “for education, health, climate protection and an affordable life,” and against any return of military conscription. Organizers said that tens of thousands participated in the protests across the country, but official figures weren’t immediately available.

In Berlin, young protesters gathered at Brandenburg Gate on Saturday afternoon, demanding more investments in education and housing.

“We call for more money to be invested in social services and education, as well as in climate protection — in short, in our future — because we are the ones who will be affected by this the longest and who will have to live with it,” high school student Lara Breitenbach said.

Janelle Schulz, another high school student from Berlin, also said that the authorities had to invest more money in education.

“At my school, the ceiling is collapsing because of water damage, nothing is being done about it, we have a shortage of teachers, the toilets are broken,” she said.

While most people rallied peacefully, some protests turned violent on Saturday night.

In downtown Frankfurt, some rioters smashed several storefronts and stole goods from inside. They also stole weapons from a gun store, which police were able to retrieve later. Some rioters also threw Molotov cocktails at police after pummeling them with stones and bottles earlier in the day, Frankfurt police said on X.

In Cologne, police ended a protest march early after protesters used pyrotechnics, threw stones at them and covered their faces despite a ban. Police also used water cannons to disperse demonstrators.

In the northern city of Hamburg, some protesters also shot pyrotechnics toward police and burned down barricades. Police used water cannons and tear gas to disperse the crowds in Hamburg.

Elsewhere in Europe, people also protested against the housing crisis and for a better future.

Thousands of protesters, including families with small children, converged in downtown Lisbon to peacefully protest Portugal’s housing crisis, holding up placards reading “Houses or Fire” and “We are not Afraid.” Others in the crowd held aloft small cardboard houses while a few dressed up for Halloween.

In The Hague, Netherlands, there was a strong police presence in and around the downtown shopping area on Saturday afternoon after online appeals for protests and fears of rioting and looting. However, there were no major disturbances by midafternoon. Many stores in the city were boarded up as a precaution.

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Kirsten Grieshaber reported from Berlin. Angela Charlton and Thomas Adamson in Paris; Kerstin Sopke and Geir Moulson in Berlin; Mike Corder in The Hague, Netherlands; and Helena Alves in Lisbon, Portugal, contributed to this report.