BRUSSELS — There were sighs of relief throughout the European Union after President Emmanuel Macron beat back a serious challenge in France from the populist far-right champion Marine Le Pen.

Then another populist went down, in Slovenia, where the country’s three-time prime minister, Janez Jansa, lost to a loose coalition of centrist rivals in parliamentary elections on Sunday.

Those two defeats were instantly seen as a reprieve for the European Union and its fundamental principles, including judicial independence, shared sovereignty and the supremacy of European law. That is because they dealt a blow to the ambitions and worldview of Viktor Orban, Hungary’s prime minister, who avidly supported both Ms. Le Pen and Mr. Jansa in an effort to create a coalition of more nationalist, religious and identitarian politics that could undermine the authority of the European Union itself.

“Europe can breathe,” said Jean-Dominique Giuliani, chairman of the Robert Schuman Foundation, a pro-European research center.

After his own electoral victory earlier this month, Mr. Orban declared: “The whole world has seen tonight in Budapest that Christian democratic politics, conservative civic politics and patriotic politics have won. We are telling Europe that this is not the past: This is the future. This will be our common European future.”

Not yet, it seems.

With Russia’s invasion of Ukraine, Mr. Orban, who has been close to both former President Donald J. Trump and Vladimir V. Putin, Russia’s president, is more isolated in Europe than in many years. He has been a model for the Polish government of the Law and Justice party, which has also challenged what it considers the liberal politics and the overbearing bureaucratic and judicial influence of Brussels. But Law and Justice is deeply anti-Putin, a mood sharpened by the war.

“The international environment for Orban has never been so dire,” said Peter Kreko, director of Political Capital, a Budapest-based research institution.

Mr. Orban found support from Mr. Trump, former Prime Minister Benjamin Netanyahu of Israel, and from the Italian populist leader and former Deputy Prime Minister Matteo Salvini. But they are all gone, as Mr. Jansa is expected to be, and now Mr. Orban “has fewer friends in the world,” Mr. Kreko said.

Ms. Le Pen’s party was given a 10.7 million euro loan in March to help fund her campaign from Hungary’s MKB bank, whose major shareholders are considered close to Mr. Orban. And Hungarian media and social media openly supported both Ms. Le Pen and Mr. Jansa.

Ms. Le Pen’s strong showing was a reminder that populism — on both the right and the left — remains a vibrant force in a Europe, with high voter dissatisfaction over rising inflation, soaring energy prices, slow growth, immigration and the bureaucracy emanating from E.U. headquarters in Brussels.

But now Mr. Macron, as the first French president to be re-elected in 20 years, has new authority to press his ideas for more European responsibility and collective defense.

After the retirement late last year of Angela Merkel, the former chancellor of Germany, Mr. Macron will inevitably be seen as the de facto leader of the European Union, with a stronger voice and standing to push issues he cares about. Those include a more robust European pillar in defense and security, economic reform and fighting climate change.

“He is going to want to go further and faster,” said Georgina Wright, an analyst at the Institut Montaigne in Paris.

But Ms. Wright and other analysts say he must also learn lessons from his first term and try to consult more widely. His penchant for announcing proposals rather than building coalitions at times annoyed his European counterparts, leaving him portrayed as a vanguard of one, leading with no followers.

“Europe is central to his policy and will be in his second term, too,” said Jeremy Shapiro, research director for the European Council on Foreign Relations in Berlin. “In the first term, he underachieved relative to his expectations on Europe — he had a lot of grand plans but failed to create the coalitions he needed, with Germany and the Central European states, to implement them.”

The Dutch, too, as the Netherlands and Germany together lead Europe’s “frugal” nations, are skeptical about Mr. Macron’s penchant to spend more of their money on European projects.

Mr. Macron “knows that lesson and is making some efforts in the context of the Russian war against Ukraine,” Mr. Shapiro said. “But he’s still Emmanuel Macron.”

In his second term, Mr. Macron “will double down” on the ideas for Europe that he presented in his speech to the Sorbonne in 2017, “especially the idea of European sovereignty,” said Alexandra de Hoop Scheffer, director of the Paris office of the German Marshall Fund.

But in his second term, she predicted, he will be more pragmatic, building “coalitions of the willing and able” even if he cannot find unanimity among the other 26 Union members.

France holds the rotating presidency of the bloc until the end of June, and one of Mr. Macron’s priorities will be to push forward an oil embargo on Russia, Ms. de Hoop Scheffer said, a move that has been complicated by the fact that many in the bloc are dependent on Moscow for energy.

The climate agenda is important for him, especially if he wants to reach out to the angry left and the Greens in France. And to get much done in Europe, he will need to restore and strengthen the Franco-German relationship with a new, very different and divided German government.

“That relationship is not easy, and when you look at the Franco-German couple, not a lot keeps us together,” Ms. de Hoop Scheffer said.

There are differences over Mr. Macron’s desire for more collective debt for another European recovery plan, given the effects of war. There is also a lack of consensus over how to manage the response to Russia’s aggression, she said — how much to keep lines open to Mr. Putin, and what kinds of military support should be provided to Ukraine in the face of German hesitancy to supply heavy weapons.

Germany is much happier to work in wartime within NATO under American leadership than to spend much time on Mr. Macron’s concept of European strategic autonomy, she noted. And Poland and the other frontline states bordering Russia have never had much confidence in Mr. Macron’s goal of strategic autonomy or his promise to do nothing to undermine NATO, a feeling underscored by the current war.

If Mr. Macron is clever, “French leadership in Europe will not be followership by the other E.U. countries, but their empowerment, by their commitment to a new European vision,” said Nicholas Dungan, a senior fellow of the Atlantic Council. “Macron can do this.”