PARIS—Jean-Luc Mélenchon has vowed to cancel hundreds of billions of euros in France’s national debt, prosecute its central-bank governor, nationalize swaths of the economy and pull out of the North Atlantic Treaty Organization.

And as student protests have washed across the country—blockading schools and, in some cases, setting them on fire—the 75-year-old Mélenchon has joined the marches or cheered them from the sidelines, drawing parallels between the students and those who stormed the Bastille prison at the start of the French Revolution.

“The Bastille has been retaken,” he said in a post on X, adding that students were “voicing their demands in the most beautiful way possible.”Now Mélenchon is emerging as the main rival of Marine Le Pen, the far-right leader and front-runner in next year’s presidential elections. Polls show the far-left firebrand elbowing past a crowded field of establishment candidates to make it into the second-round runoff with Le Pen. Mélenchon is raising the possibility of a presidential contest defined by the far ends of the political spectrum.

While his rhetoric is energizing part of the French electorate, Mélenchon’s confrontational style and radical economic proposals have spooked much of the country. Le Pen would easily win in a runoff against Mélenchon, leading 67% to 33%, according to a survey this week by pollster Toluna Harris Interactive.

“A second-round face-off between Mélenchon and Le Pen is the ultimate nightmare scenario,” said Philippe Pouletty, who heads Truffle Capital, a Paris-based venture-capital firm.

Mélenchon was born in Morocco to French parents, moved to France as a child and later studied French literature and philosophy at the university of Besançon, in Eastern France. He took part in the student protests that rocked French universities in 1968.

After graduating and entering politics, he joined the Socialist Party, where he stayed for more than three decades serving in various posts. In 1986, when he was 35, he became the youngest French lawmaker to be elected to the Senate.

He left the Socialist Party in 2008 to establish his own political party, the Left Party, which later became France Unbowed. Over the past decade, he has transformed the party from a fringe movement into a force in French politics.

This is his fourth run for the presidency. He has positioned himself as a champion of the banlieues, France’s working-class suburbs, by focusing on issues such as discrimination against minorities and police violence.

“The high-school student movement is a godsend for Mélenchon,” says Olivier Costa, a research professor at the Paris-based Sciences Po university and the National Center for Scientific Research. Mélenchon is trying to build momentum behind it and present himself as the candidate of the youth, he added.

In response to the school protests, Mélenchon has promised to make big increases in the French education budget, hire more teachers and raise their salaries. He has said he would hold police accountable as the protests have turned violent, leading to severe injuries among some protesters. One teenager’s hand was blown off by a dispersal grenade, another lost an eye, while a 14-year-old boy suffered a jaw fracture.

He has drawn criticism in recent weeks from other political leaders, who have accused him of fueling the protests for political gain. Gabriel Attal, a centrist presidential candidate and former prime minister, said last week he understood the frustration of high-school students but he blamed Mélenchon for fanning the flames. He is “legitimizing violence, calling for riots, and turning young people into political cannon fodder,” Attal said.

Mélenchon has called for an economic overhaul of France. He wants to increase the minimum wage, cap prices on fuel and essential goods, lower the age of retirement to 60, and adopt a wealth tax on the assets of people with net wealth of at least 100 million euros, equivalent to $112 million. He proposes deep investments in green technologies to implement what he describes as an “ecological bifurcation.”“It’s about reversing the current logic,” said Éric Coquerel, a France Unbowed lawmaker and a lieutenant of Mélenchon. He said Mélenchon wants to pursue economic stimulus rather than what he described as the disastrous supply-side economics of President Emmanuel Macron.

One of his Mélenchon’s most controversial ideas has been his proposal to freeze or wipe away the French bondholdings of the Bank of France, a sum worth €488 billion. Coquerel said the measure would considerably reduce France’s debt-to-GDP ratio and ease some of the pressure on its finances.

Economists warn such a move risks calling into question the independence of the European Central Bank and that it would have no real impact on the government’s public deficit.

“It’s pointless,” said Xavier Timbeau, an economist at OFCE, a Paris-based, state-funded economic observatory. The French government owns the central bank. That means the interest the government pays on the debt the bank holds ultimately goes back to state coffers as dividends, he said.

Mélenchon has described calls for the urgent reduction of France’s deficit as scaremongering by the government to push through austerity measures. In recent days, he has engaged in a war of words with Bank of France Governor Emmanuel Moulin, after the official warned the country risked being strangled by interest rates if it didn’t clean up its public finances.

In a post on X, Mélenchon called Moulin’s warnings an act of treason and threatened to prosecute him.

“I won’t let myself be intimidated,” Moulin said in a subsequent radio interview, adding he would continue to speak his mind and defend the institution he leads.

“We’ll see about that,” Mélenchon said at a rally Sunday, warning the central bank governor: “Keep your mouth shut.”Mélenchon’s position on the war in Gaza has also sowed division within the left. Following the deadly Oct. 7 attack led by Hamas, he refused to describe the group as a terrorist organization. He became a critic of the Israeli government, calling its war in Gaza a genocide, and placing the issue at the center of his party’s campaign for the 2024 European elections.

Other left-wing leaders accused Mélenchon of being driven by electoral calculations and turning a blind eye toward antisemitism. His refusal to attend a nationwide march against antisemitism in Paris only bolstered such accusations. Mélenchon denies that he is antisemitic.

Raphaël Glucksmann, who won France’s center-left presidential primary on Sunday, ruled out any alliance with Mélenchon’s France Unbowed.

Mélenchon has also faced criticism within his party. Over the last two years, key figures have left France Unbowed describing an absence of internal party democracy, alleging that Mélenchon exercises absolute control and sidelines anyone who questions his decisions.

Raquel Garrido, a former lawmaker and longtime Mélenchon aide who was expelled from France Unbowed two years ago, said he made unifying left-wing parties impossible, effectively undermining the left’s chances of winning the presidential elections. “Paradoxically, Mélenchon is accelerating the rise of the far-right,” Garrido said.

Write to Noemie Bisserbe at noemie.bisserbe@wsj.com