AMNA NAWAZ: Well, protests are continuing in France a day after more than 250,000 people took to the streets across the country to demand education reforms.

Demonstrations began in mid-September, fueled by frustrations over classroom sizes and poor building conditions.

Nearly 500 people were arrested Tuesday, bringing the total to more than 6,000 since the start of the protests.

Special correspondent William Denselow reports from Paris.

WILLIAM DENSELOW: Anger on the streets of Paris, as demonstrators led by high school students continue to give French authorities a failing grade.

MARWAN, Student (through translator): National education is really catastrophic.

Personally, in my high school, the roofs are open, there's no heating, the desks are broken.

So we work in really precarious conditions.

RAYAN, Student: The building, the school and the system, we want to change.

WILLIAM DENSELOW: The government says demonstrations have been hijacked by outside groups, leading to urban violence.

Several hundred teenagers have been injured, prompting authorities to suspend the use of stun grenades.

AMAIMA, Student: A boy whose mouth is completely destroyed, et cetera, and many more things.

And it's just horrible to see, especially when it's kids who are just trying to fight for their rights.

WILLIAM DENSELOW: A right to a better education.

France tops the list for average class sizes in Europe, with roughly 25 to a class in public schools from ages 11 to 15.

Responding to the recent protests, the government promised to make visible changes to the nation's schools.

EDOUARD GEFFRAY, French Education Minister (through translator): We must do more and better, notably for high schools.

And so the prime minister has entrusted us with a number of initiatives.

WILLIAM DENSELOW: Initiatives like addressing class cancellations by replacing absent teachers.

But that requires substantial investment, no easy task as French public debt hit roughly $4 trillion in June, soaring to 119 percent of GDP.

That's the highest level since 1946, after the destruction of World War II.

GENEVIEVE PONS, President, Europe Jacques Delors: Times are difficult with oil prices rising.

So it's a really difficult moment for the government in France now, because they have to face these real problems with very rapidly shrinking means.

WILLIAM DENSELOW: For demonstrators, the message is clear.

Lawmakers must find a solution.

Trade unions joined Tuesday's demonstrations in solidarity with the student movement.

It adds further pressure on the French government ahead of next year's presidential elections.

Genevieve Pons, president of the Europe Jacques Delors, a Brussels-based think tank, says whoever is elected president next April will be tasked with answering a fundamental question.

GENEVIEVE PONS: France will need total, if I may say so, rethinking,because we have to answer this question.

Why is it the country where the taxes are the highest and a country where public services have real problems?

WILLIAM DENSELOW: Existential questions attracting attention from overseas.

On Tuesday, President Trump weighed in on social media, claiming the protests were being fueled by out-of-control mass migration and not schools, further stoking an already charged immigration picture here.

In response, the French foreign minister said France will write its own story during what's becoming an increasingly challenging chapter in the country's history.

For the "PBS News Hour," I'm William Denselow in Paris.