There are other, more stable leaders whose roles in Europe could grow to meet the crisis. But they have complications of their own.

Keir Starmer, who was elected prime minister of Britain in July, has already been bruised by public outcry over gifts that he and his wife accepted – and his country is not in the European Union.

Giorgia Meloni, the Italian prime minister, is a populist who could forge a close relationship with Trump – or who could find her relatively centrist approach to international affairs and support for Ukraine at odds with Trump’s own positions.

Analysts agree the most natural fits to lead a more independent, muscular Europe would need to come from Berlin or Paris, the places now most troubled.

“There is a very clear crisis of Franco-German leadership that is intensifying with the collapse of the German coalition and with France self-absorbed by its own internal political divisions,” said Alexandra de Hoop Scheffer, president of the German Marshall Fund of the United States in Paris. “And that’s a handicap on the European and international stage.”

Jörn Fleck, a senior director with the Europe Centre at the Atlantic Council in Washington, said France and Germany were suffering from “self-inflicted” political crises just as Trump’s election added large new uncertainties to Europe’s future.

“We’re looking at a much more challenging relationship,” he said. “Things might get worse quickly before they get better.”

Macron and Scholz acknowledged that difficulty this past week but offered few clues as to how they might rise to meet it.

Trump “was elected by the American people, and he’s going to defend the interests of the American people – that’s legitimate and a good thing”, Macron said on Thursday at the opening of a summit of European leaders in Budapest, Hungary. “The question is, are we ready to defend the interests of Europeans?”

The world is made of herbivores and carnivores, he added, and “if we decide to remain herbivores, the carnivores will win”.

Scholz acknowledged the challenging timing of his decision to kill his coalition by expelling his finance minister, Christian Lindner, who had begun to undercut the government’s economic agenda.

Instead of staying in office through next year’s regularly scheduled elections in the third quarter, Scholz and his coalition will now probably face voters in March – and Scholz appears likely to lose the chancellorship.

“I would have liked to have spared you this difficult decision, especially in times like these, when uncertainty is growing,” Scholz said.

But, he added: “We must stick together in Europe more than ever and continue to invest together in our own security and strength. Because the situation is serious.”

For years, Macron has repeatedly urged Europe to be more united and more independent militarily, economically and technologically – less tethered to the whims of successive US administrations and better equipped to compete with China’s industrial and commercial dominance.

But he is now in a much weaker position than he was during his first term – a near lame duck who no longer has much control over domestic policy and who is term-limited, as he cannot run for office again in 2027.

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The French government is mired in parliamentary debates over a budget that is badly needed to rein in ballooning deficit and debt that are some of the worst in Europe. It is still unclear whether the government will be able to secure the deep spending cuts and higher taxes it is seeking by the end of the year without collapsing.

A different, but no less divisive, budget debate looms this week in Germany. Leaders will need to agree on steps to plug a budget hole and comply with what is essentially a constitutional mandate for balanced budgets outside of times of emergency.

Disagreement over how to do that – and how best to use fiscal policy to shock the German economy out of recession – helped drive the split in Scholz’s coalition.

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An even bigger fight could be just around the corner. Trump has pushed for Germany to spend more on its military, which would require Berlin to increase its defence budget, and which would come with its own risks.

That would force leaders to take new steps to borrow money – or to ponder politically painful domestic spending cuts to free up more money for the military, which could stoke voter outrage and help “Germany first” parties, such as the far-right Alternative for Germany, at the polls.

Scholz has expressed a preference for borrowing, and rejected spending trade-offs. The heavy favourite to lead the next government is the major mainstream alternative to Scholz’s Social Democrats: the more conservative Christian Democrats. They would change some policies but remain strong Ukraine supporters. If they or another mainstream party can form a government, analysts say, that may end Berlin’s policy paralysis – at least for a while.