Ms Marine Le Pen has put on a courageous face following her crushing defeat to Mr Emmanuel Macron in the presidential election, pledging to overhaul her far-right party and turn it into the main opposition to France's new centrist leader.
According to the French Interior Ministry, Le Pen lost to independent Emmanuel Macron on Sunday with 33.9 percent of the votes against his 66.1 percent.
"I am happy with the result of Emmanuel Macron being elected president, which constitutes a veritable relief for all our nation and for the Jewish community of France", Joel Mergui, the president of the Consistoire, wrote Sunday evening in a statement by his group, which is responsible for providing religious services to Jews.
Macron handily defeated far-right National Front leader Marine Le Pen in Sunday's presidential runoff, and now must pull together a majority of lawmakers for his year-old political movement to run in the mid-June legislative election.
"I will be candidate for the presidential majority and I wish to join the list (of candidates) of his movement", Valls, a Socialist, told RTL radio.
Macron, 39, founded his centrist En Marche (On The Move) movement of mostly political neophytes just a year ago on a promise to inject new blood into France's discredited political class. He clinched 18 percent of the vote in the 2002 presidential elections - the first time that National Front made it to the final round. But a high number of blank or spoiled votes and unusually low turnout are signs of an electorate dissatisfied with its choices.
France's Macron lays groundwork for transition to presidency
Le Pen responded to defeat by vowing she would lead her anti-immigration National Front (FN) strongly into the legislative elections.
Hollande's term as president expires May 14 midnight.
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. Sylvie Goulard, a French deputy to the European Parliament, said Macron would make Berlin his first official visit, with perhaps a stop to see French troops stationed overseas as well.
The anti-European Union, anti-immigration party will now focus on next month's parliamentary elections, although Ms Le Pen recognised that the party needs far-reaching change.
In Britain, Prime Minister Theresa May said Macron's win makes it even more important for British voters to back her Conservatives in the early election she called for June 8, to strengthen Britain's hand in its divorce proceedings with the EU.