Brussels  -  Three months from now, 370 million Europeans will be called to elect a new EU parliament under the shadow of a contest playing out across the Atlantic, as Donald Trump fights to reclaim the White House.

How exactly the prospect of a Trump 2.0 presidency -- growing more tangible by the day -- could nudge voters across the 27-nation European Union one way or another, is an unknown.

But one thing is certain: it would have a major impact on the bloc -- at a crossroads when it comes to fighting climate change, shoring up Ukraine against Russian aggression, and ensuring its own security.

"For Europe, Trump 2 is both a huge exclamation mark, and a huge question mark," said Sebastien Maillard, associate fellow at the London-based think-tank Chatham House.

Graphic explaining the voting system for the European election

Trump's disruptive first term -- with his "America First" credo dismissing multilateralism in general, and the EU in particular -- is still fresh in European minds.

The twice-impeached politician has causes consternation in Europe with his threats to walk away from America's NATO commitments, fuelling a push by Brussels towards greater security independence.

"The Trump scenario is very, very consequential for what the European project is going to be able to do over the next period," said Susi Dennison, senior policy fellow at the European Council on Foreign Relations (ECFR).

Any number of the bloc's strategic priorities become "much, much harder to achieve" with him returning to power, she added.

European elections: the voting system

- Sharp turn right -

On the most critical of these -- the conflict on the EU's eastern rim -- US Republicans are, at Trump's behest, blocking vitally needed aid to Ukraine. They have maintained that position despite warnings that this could hand the advantage to Russia.

While the EU seeks to spearhead the global fight against climate change, Trump's second term plans tack radically the other way: he vows to tear up a massive clean energy bill.

Both European priorities -- preserving Western unity on Ukraine and transitioning to carbon neutrality by 2050 -- could already be complicated by the June 6-9 European Parliament vote.

The far-right in the outgoing European Parliament

The balance of power in the 720-seat legislature determines how the EU's top jobs -- heading the commission, the parliament and the European Council, and leading foreign policy -- are shared out.

Indicators suggest a surge by far-right parties, fuelled by anti-establishment currents coursing across the bloc.

The centre-right European People's Party is set to remain the biggest force, followed by the Socialists -- but the centrist Renew Europe could lose third place to the far-right Identity and Democracy group.

The ECFR predicts "anti-European populists" will likely come out on top in nine member states including France, Hungary, Italy and The Netherlands.

Composition of the outgoing European Parliament

- Trump playbook -

ECFR polling shows Europeans across the bloc are most animated by the cost-of-living crisis: more than three in four expect their living standards to fall this year, according to a Eurobarometer poll from December.

Inflation is sinking back down from record highs, but European growth is still flatlining -- it is forecast at 0.6 percent this year in the eurozone -- with no rebound in sight.

"Clearly the economic situation matters everywhere," said the ECFR's Dennison. His view is that populist movements have been more effective in harnessing economic frustrations -- and in many cases putting the blame on climate action.

Trump in many ways provided the playbook for Europe's expanding far-right, said Rachel Rizzo, senior fellow at the Atlantic Council's Europe Center.

Key facts on representation in the European Parliament

"You see a shared language," she says. "You hear terms like 'wokeness', like 'fake news' that originated from Donald Trump, and they're used by parties in Europe."

Does that mean Trump could seek to weigh in on the EU election debate?

His decision to host Viktor Orban at his Florida Mar-a-Lago resort this week does send a message: the Hungarian prime minister is the only EU leader to maintain close ties to the Kremlin, and seems to revel in tripping up the bloc at every opportunity.

But for Chatham House's Maillard, if by June Trump is realistically tipped to defeat Joe Biden, that "unsettling" prospect may ultimately favour European establishment parties.

"The more Trump becomes a threat, and the more Russia turns aggressive, the less people are going to want to jump into the unknown," Maillard said.

Main features and powers of the European Parliament

"Railing against Brussels bureaucracy, rules and regulations -- the far-right knows how to do that," he said.

"But when it's about Europe versus the rest of the world -- that's a different matter."

By Emma Charlton and Jerome Cartillier

Infographics by Julie Pereira, Herve Bouilly, Sabrina Blanchard, Valentina Breschi & Guillermo Rivas Pacheco