PARIS—The riots sweeping France have rocked the country’s political establishment, but one person is positioned to emerge from the chaos with a stronger hand: Marine Le Pen.

For more than a decade, the far-right leader has cast France as a nation adrift, buffeted by waves of immigration and lawlessness that have torn at the country’s social fabric. As bands of hooded rioters in dark clothing have descended on city centers across France, raiding city halls and looting thousands of stores, Le Pen has sought to present herself as the sole candidate in this spring’s presidential election willing to restore order.

The strategy was on display this week as Le Pen released a video address that bore the hallmarks of a president addressing the nation. Seated at a desk before an august bookcase and flanked by France’s tricolor flag, Le Pen cast the riots as a crisis of faith in President Emmanuel Macron’s authority.

“Our country is caught in a vice, held hostage between violence and powerlessness,” Le Pen said. “In six months, the French people will be able to choose a different path—one of authority and restored security.”The approach has given Le Pen an air of inevitability as she pursues France’s highest office.

“It’s as if she’s at the office, already at the Élysée Palace,” said Adélaïde Zulfikarpasic, a pollster at the French polling firm Ipsos Bva.

Le Pen’s long-running focus on law and order, Zulfikarpasic said, allows her to position herself as a guarantor of stability when democracy itself is in crisis.

“People no longer have confidence in the state to ensure their protection and meet their needs. And she’s contrasting with that,” she said.

The riots are working to Le Pen’s advantage in other ways. As the violence has flared, Jean-Luc Mélenchon, the far-left firebrand running for president, has dominated headlines with his support for protesters, drowning out establishment candidates and bolstering his chances of reaching the second-round runoff with Le Pen. If he succeeds, polls show, Le Pen would beat him handily.

Raphaël Glucksmann, the socialist candidate competing with Mélenchon, described him as a “steppingstone for the far-right, because who is going to benefit from this chaos if not Madame Le Pen.”Le Pen has underperformed in previous presidential elections, riding high in the polls as the first round of voting approached, only to lose by a wide margin in the runoff as voters who supported other candidates coalesced around Macron. This time, however, Macron is term-limited. Le Pen’s newfound status, meanwhile, marks something of a role reversal.

The party that Le Pen inherited from her father, Jean-Marie Le Pen, was long regarded as a risky, antiestablishment force that couldn’t be relied upon to govern France and ensure its economic stability. He drew condemnation for repeatedly minimizing the Holocaust and was expelled from the party by his daughter in 2015 for his views. Le Pen herself spooked voters when she first ran against Macron in 2017 with her pledge to pull France out of the euro, the continent’s single currency.

Nearly a decade later, Macron is the one under pressure to reassure France and global investors. His governments have been running deficits above 5% of GDP for years, sowing doubts about whether France can repair its finances and pushing up the country’s borrowing costs. The country’s debt pile is nearly 120% of gross domestic product.

Le Pen and her party, National Rally, have played a role in the fiscal mess, voting to oust two of Macron’s prime ministers who sought to introduce spending cuts and rein in the deficit. Le Pen is also campaigning on a pledge to lower France’s retirement age to as low as 60, a move that would add billions to the country’s annual deficit.

Le Pen’s economic record, however, is now largely overshadowed by the riots and the crisis engulfing Macron’s final months in office.

The protests have escalated from a student-led set of complaints over conditions in schools into a broader movement driven by grievances over the cost of living, cuts to public spending and dissatisfaction with government.

On Monday, Macron’s office said his interior minister, Laurent Nuñez, had offered his resignation, but the president had declined it because of the need for stable leadership. The government then announced it was imposing a curfew in shopping districts and other rioting hot spots. More than 3,000 stores were damaged or looted nationwide over the weekend, authorities said, adding that affected businesses would be eligible for state aid to temporarily pay their staff.

“The social instability over the weekend absolutely plays into Le Pen’s campaign that the establishment has delivered chaos and now is the time to try something different,” said Mujtaba Rahman, head of Europe for risk analysis firm Eurasia Group.

Rahman said Le Pen ultimately aims to persuade voters that she “is not the risk, voting National Rally isn’t the risk. The risk is coming from the established parties that are failing to deliver on the economy.”Le Pen’s anti-immigration stance, meanwhile, gives her another way to frame the unrest. Le Pen has cast the unrest as the work of far-left radicals allied with youths from France’s banlieues, the poor urban outskirts where much of the country’s minority Muslim population resides.

[video] Flames Scorch Historic Streets and Buildings as French Protests Erupt“The looting drew attention to a segment of the population—specifically young people from certain neighborhoods, some of whom are from immigrant backgrounds,” said Zulfikarpasic, the pollster. “And that hits the themes at the heart of National Rally’s rhetoric.”As Le Pen approaches the final stretch of the campaign, however, she faces a legal minefield stemming from her 2025 conviction for misusing European Parliament funds.

Le Pen has denied any wrongdoing. In July, an appeals court upheld the ruling, sentencing her to a three-year prison term, with two of the years suspended. The remaining year, judges said, could be served wearing an electronic bracelet, raising the possibility that Le Pen will have to campaign under judicial surveillance.

Write to Stacy Meichtry at Stacy. Meichtry@wsj.com