Meanwhile, Germany's election campaign is beginning to heat up ahead of September's vote, and Italy is also due to hold an election by the end of May 2018 at the latest.
Some in Brussels will try to argue that in the wake of May triggering Article 50
, the UK election is a distinct affair with no implications for the future of the wider EU -- which remains united -- but there could be considerable indirect effects.
The situation in France is intriguingly poised
, with it looking increasingly likely that any combination of the four leading candidates -- far-right Marine Le Pen
, centrist liberal Emmanuel Macron, conservative François Fillon or far-left Jean-Luc Mélenchon -- could end up facing each other in the second round of voting.
Any small shifts in the final days of the campaign could have huge bearing on which candidates make the final two.
One scenario likely causing sleepless nights in Brussels is a Le Pen-Mélenchon head-to-head: Although coming from opposite sides of the political spectrum, both have suggested they would consider dropping the euro
and both want to renegotiate radically the terms of France's EU membership before putting the question to a referendum.
If Le Pen and/or Mélenchon make it into the second round, the French and British elections could overlap. Le Pen in particular has tried to make herself appear more credible and mainstream by praising May's leadership in the wake of the Brexit vote and has said that May is
"running the UK using policies that I want to run" -- i.e., a greater degree of intervention in the economy and a reduction in immigration.
The lack of an immediate Brexit-induced economic downturn also serves as a useful foil for Le Pen when defending her controversial plans to replace the eurozone with a basket of new national currencies and giving the government direct control over the central bank, allowing her to argue that
"all those who predicted apocalypse (post-Brexit) got it wrong."
Interestingly, this could become a two-way interaction with the French elections also affecting the UK debate. Continuity Remainers and "soft Brexiteers" will be backing an establishment figure such as Macron on the basis that his election will be more likely to lead to a close and friendly post-Brexit UK-EU relationship, while those who want not only for the UK to leave the EU but for the EU to unravel completely will be cheering on Le Pen and/or Mélenchon.
It creates another headache for May, who will need to strike the right balance between rallying grass-roots supporters and keeping the anti-EU media on the side while also preventing election rhetoric getting out of hand and poisoning the formal Brexit negotiations. Any indication that Brexit is fueling support for the likes of Le Pen and thereby threatening the very existence of the EU will make it harder for the UK to secure a favorable exit deal.
Meanwhile, over in Germany, the main contest will be between Angela Merkel and Martin Schulz, both of whom are committed to further European integration. Unlike France, there is no prospect of a radical outsider winning and fundamentally changing the country's direction. That said, despite a number of setbacks and a backdrop of near constant infighting, the nationalist Alternative for Germany is almost certain to win parliamentary seats.
In Italy, the situation is more pressing, with parties that back the country's exit from the eurozone -- ranging from the far-right Lega Nord to the catch-all populism of the Five Star Movement -- attracting more and more attention.
Given the Italian economy has barely grown in real terms since adopting the euro, conditions are ripe for a populist backlash. Although not all supporters of these parties would definitely back a messy euro exit, the mere prospect of an Italian referendum on euro membership could send markets into panic.
One big difference between anti-EU sentiment in the UK compared with elsewhere on the continent is the lack of credible establishment backing of the sort able to propel Brexit from a cause with significant minority support to a proposition able to get more than 50% in a national referendum.
Therefore, the image of May, a credible and popular leader deploying anti-EU rhetoric on the campaign trail en route to winning a thumping parliamentary majority, should be a cause for concern from the perspective of Brussels.
If Brexit comes to be generally seen as a success, it will become harder for the Brussels establishment to dismiss it as a minority view limited to the fringes of UK politics.
And while a May victory might not bolster the credibility of Le Pen and Alternative for Germany enough to win them national elections in the short term, it will give those who only last month signed a fresh treaty committed to the future of European unity
a huge headache in the long term.