Pieter Cleppe is the head of the Brussels office of Open Europe , an independent think tank specializing in policy in Europe and the European Union. The opinions in this article belong to the author.

(CNN) France has spoken, for now. The country voted yesterday in the first round of its presidential elections, after weeks of campaigning that have been dogged by scandals, gaffes and surprises .

Though the first round treated voters to 11 candidates to pick from, in the year following Britain's decision to leave the European Union and American voters sending Donald Trump to the White House, one candidate has dominated media coverage: the populist, nationalist, far-right Marine Le Pen

As had been expected for some time, Le Pen has made the final round, where she will face the centrist Emmanuel Macron. Macron's centrism and pro-European leanings will now inevitably frame the run-off as an effective referendum on France's future relationship with the EU. As a founding EU member, this will likely be giving political leaders in Brussels reason to worry.

Le Pen's National Front Party has a long history of euroskepticism and promotes a number of policies that are anathema to the high-minded principles behind the European project.

In recent years, Le Pen has attempted to soften both her image and the position of her party on the matter of France's future in the EU.

At one time, the National Front was in favor of abandoning the euro, plain and simple. More recently, she has said she would organize a referendum on France's common currency membership.

Now, she has specified that she would try to renegotiate France's EU membership over six months. If that attempt fails, she'll hold a referendum

Could she hold a referendum, and what could happen if she does?

Even if she does win the presidency, Le Pen would be wise to keep the champagne on ice for a while. She is unlikely to get a majority in the French parliamentary elections, due to be held June 11, and would therefore face a hostile -- probably center-right -- government standing in the way of executing her plans -- and holding a referendum.

Still, she would able to call a nonbinding referendum without the approval of the government.

If the French people were to vote to keep the euro -- which is likely if you believe French opinion polls -- she would stand down, given then that "70% of my project cannot be put in place."

If a majority in France voted to leave the EU and the eurozone, it's constitutionally illegal for France to leave, as its constitution states " the Republic is part of the European Union. " So a French EU exit would require a burdensome constitutional change.

Frexit and the economy

Of course, all of these legal considerations regarding EU membership will be of minor importance should France actually decide to leave the eurozone. The economic chaos it would likely cause would be the top priority for everyone in France and across the continent.

The French Central Bank has estimated that refinancing French public debt outside of the eurozone would cost more than 30 billion euros ($32 billion) in additional annual interest.

JUST WATCHED Pressure mounts on leading French candidates Replay More Videos ... MUST WATCH Pressure mounts on leading French candidates 04:22

According to Le Pen , exit from the euro would not result in economic "catastrophe." She has stressed she wants France to leave the eurozone in the best possible circumstances, saying she does not want to "break the dishes," and suggesting it should happen through consultation with other European countries she considers to be "suffering" from euro membership, predicting that Italy, Spain and Greece would join France.

Even a moderate President Le Pen is trouble for EU

If France votes to stay in the eurozone but Le Pen doesn't stand down, some of her other proposals are hard to square with anything for which the EU stands. Look at her protectionist proposals, such as imposing an import tax of 3%.

Everything really would be on the table if Le Pen is elected, given the political damage it would do to the EU and the eurozone: projects that are completely reliant on political goodwill.

With regard to Schengen , things may get serious right from the start. She has just made clear that, if elected, she would immediately suspend France's membership of the border-free zone.

The European Commission has already stretched the possibility of suspending Schengen, but proper border checks -- with all the traffic jams they would cause, as witnessed when they were implemented between Croatia and Slovenia some weeks ago -- are bound to create a lot of economic damage right away.

Brussels may have avoided what German Finance Minister Wolfgang Schauble called the nightmare scenario of the final round being between Marine Le Pen and left-wing Euroskeptic Jean Luc Mélenchon.

But even if Le Pen is ultimately thwarted, the success of her campaign and the flames it has fanned will ensure that any celebrations are short-lived.