“The experienced politicians were rejected and now we have a new category of candidate,” said Dominique Bussereau, a member of the mainstream right party Les Republicains.

But for all the turmoil, whether either candidate will be able to muster broad legislative or popular support is in doubt — raising the real possibility that an election intended to shake the status quo could still result in stasis. Can either candidate, as an outsider, really be effective as president?

Neither has ever held national elected office. Each lacks any real base of support in Parliament and will be trying to build one from the ground up. The president of France is powerful only if he or she has a majority in Parliament to help push through his or her party’s program.

That uncertainty may ripple through Europe, which will be watching closely to gauge both the strength of far-right forces in France and the depth of the anti-European Union sentiment.

The differences between the candidates are so deep that the winner will surely be seen as a harbinger of Europe’s future. Resentment of European Union rules and the failure of the bloc to wrestle with immigration and border controls were major issues in the campaign.

Beyond France, the election will be critical in determining Europe’s openness to the world and the fate of its generous social welfare benefits. It is being especially closely watched in Germany, which holds parliamentary elections in September, as well as in Italy, which could also hold elections this year.

In particular, a close eye will be kept on Ms. Le Pen’s share of the vote, which will serve as a gauge of the current strength of the populist tide that last year ushered Britain’s vote to leave the European Union and Donald J. Trump to power in the United States.