President Emmanuel Macron has suffered a bruising setback in France's politics but may yet stay out ahead in a three-way race as Europe's informal leader, not because of his own mandate but because of the weakness of his German and Italian rivals.

Nonetheless, just as he is having to learn new negotiating skills in Paris after a parliamentary election setback on Sunday, he may have to become more accommodating in Brussels and other European capitals, from his fiscal ambitions to his defense goals.

His "domestic issues will follow him everywhere," one diplomat from a country where ruling coalitions are the norm told Reuters.

In France voters traditionally hand their presidents a majority in parliament.

But with Macron now negotiating with opposition parties to break an impasse, he may have to take on board their thoughts on Europe too if some of them join a coalition, even if the constitution gives the president the lead on foreign policy.

A first test of any impact to his standing among the European Union's 26 other leaders will come on Thursday when he travels to Brussels for an EU leaders' meeting. G7 and NATO summits then follow in quick succession.

"I expect that Macron is going to continue to exert leadership because there aren't really any other leaders in Europe who have an agenda for Europe," Georgina Wright of the Institut Montaigne think-tank told Reuters.

German Chancellor Olaf Scholz has struggled to express a coherent vision for the bloc and match the influence enjoyed by his predecessor Angela Merkel, in part because of his own four-party coalition in Berlin.

In Italy, the EU's third-largest country, Prime Minister Mario Draghi also has to contend with unstable coalition partners who may yet trigger a government collapse before next year's scheduled parliamentary elections.

However, one German government source said Berlin eyed an opportunity to rein in the Frenchman's fiscal ideas - such as his openness to future mutualized debt and more flexible deficit rules.

"The election result might have a positive effect: Macron won't be able to push through his fiscal policy ideas in EU - especially if he lines up with the conservatives who are very strict on this issue," the German official said.

AUTHORITY CHALLENGED

Macron's domestic woes come at a time when Russia's war in Ukraine, an energy crisis and the spiralling cost of living are challenging the authority of the bloc's leading three statesmen.

Macron's advisers dismiss any suggestion that the results of Sunday's vote will diminish the French leader's ability to shape the European agenda.

"What I'm getting from contacts in the European capitals is more curiosity about the meaning of the vote in the context of French parliamentarism than concerns about France's capacity to exert leadership in Europe," an Elysee official said.

In Rome, Foreign Affairs Undersecretary Benedetto Della Vedova described Macron as "the leader with the most experience".

"If he is clever he will form a more varied, but not necessarily more fragile, parliamentary majority, and France's role as a driving force in the EU will remain," Della Vedova said.

A senior Eastern European official said it was too early to determine how, if at all, Macron's domestic troubles will play out on the European stage.

However, he cautioned that the French president's pro-European message could be drowned out by the enlarged presence of two euro-sceptic parties on the far right and hard left in France's parliament.

Marine Le Pen's far-right Rassemblement National may have dropped its calls for a Frexit, but it calls instead for a Europe of sovereign nations, while Jean-Luc Melenchon's far-left party says France should "disobey" EU rules. Both won their biggest number of lawmakers on Sunday.

"In my experience the mandate you have does matter," the Eastern European diplomat said.