He also invited President-elect Macron to visit Singapore. If he does, he would be able to pick the candidate of his choice to lead the government as prime minister.
Her tally was nearly double the score that her father Jean-Marie, the last far-right candidate to make the presidential runoff, achieved in 2002, when he was trounced by the conservative Jacques Chirac.
Macron, a 39-year-old centrist, won 66 percent of the vote in the May 7 election, beating Le Pen following a divisive runoff vote between two candidates with diametrically opposed visions for the country's future.
"I will fight the divisions that undermine France", he added in a nod to the 11 million votes Le Pen received, a record for the far-right leader.
On Monday, though, Hollande gripped Macron's arm before the two men walked side by side and then announced the transfer of power would take place on Sunday, a week after the election.More news: Barclays Center to host 2017 NBA Draft for fifth-straight year
Macron will on Tuesday mark the EU's Europe Day, the annual celebration of peace and unity in Europe.
The vote was the best electoral result ever obtained by her National Front party, which was established in the 1970s by her father, the Holocaust denier Jean-Marie Le Pen, who has multiple convictions for inciting racial hatred against Jews. "He's got 24 hours", Griveaux said.
"The National Front is a tool that will evolve to be more efficient, bring even more people together after the number of voters we reached last night".
German Chancellor Angela Merkel welcomed his win, but appeared cautious about proposals to support his economic plans either by relaxing European spending rules or with a dedicated stimulus fund.
It's also a further dent to the populist tide that many blame for Britain's vote to leave the European Union and the election of Donald Trump as US president.
Francis Kalifat, president of CRIF, called the victory "incontestable" and congratulated Macron on it. In total, 28 per cent of Catholics voted for Fillon, compared to 22 per cent each for Macron and Le Pen. Other indexes across Europe were also trading lower, while the euro, which briefly hit a six-month high above $1.10 overnight, was down 0.5 percent at $1.0942.