Russian President Vladimir Putin on Monday told French President-elect Emmanuel Macron that the two countries should end their "mutual mistrust".
They had feared another populist upheaval after Britain's vote to exit the European Union and Donald Trump's election as U.S. president a year ago.
With the two mainstream parties - the conservative Republicans and the left-wing Socialists - both failing to reach the presidential runoff vote, his chances of winning a majority that supports his election pledges will depend on him widening his centrist base.
"He carries the hopes of millions of French people, and of many people in Germany and the whole of Europe", German Chancellor Angela Merkel told a news conference in Berlin.
Other world leaders from Canada to Latin America to Australia also congratulated Macron on his historic victory. "France is one of our closest allies and we look forward to working with the new President on a wide range of shared priorities".
Eurosceptics have been on the rise on a continent badly rattled by the eurozone debt crisis and the mass refugee influx that peaked in 2015 and angered especially eastern European Union members on the so-called Balkans route.
The legislative election will take place on June 11 and June 18.
However, the tide appears to be turning this year, starting with the defeat in March in the Netherlands of anti-Islam candidate Geert Wilders.More news: Protester killed, AP journalist wounded in West Bank clash
European Commission chief Jean-Claude Juncker wrote on Twitter that he was "happy that the French chose a European future". Quarter-final: "Stable Netherlands. Semi-final: "La France en Marche!".
Party, won France's presidential election on Sunday.
"I will be at the head of this combat", she said.
Should En Marche! not emerge as the largest single group in June's elections, France would enter a period of "cohabitation", which would require Macron to appoint a prime minister outside his party.
The victory was remarkable in many ways.
Martin Quencez of think-tank the German Marshall Fund of the United States argued that in France "the structural issues behind the populist votes are yet to be tackled".
Success for Le Pen also came in the ambiguous attitude of the charismatic radical-left candidate Jean-Luc Mélenchon, who refused to tell his nearly 20 percent of voters what to do in the second round, leading many of them to reject both the far-right and the liberal finalists. If it does it's yet another kick in the guts for the political establishment, which should give Bill English pause for thought.
When Macron announced that he was going to visit striking workers at a factory in eastern France who were fighting against the closure of their workplace and its transfer to low-wage Poland, Marine Le Pen rushed to get there before him, promising the workers they'd keep their jobs in France, and taking selfies with them, before leaving to the sound of applause.