Macron's election in a victory over the National Front's Marine Le Pen on Sunday has destroyed the dominance of the center-left and center-right parties which have ruled over French politics for almost 60 years.
Modi had yesterday greeted Macron for his electoral win in a tweet.
There is scepticism about Macron's ability to win a majority with candidates from his En Marche movement - "neither of the left, nor right" - alone, meaning he might have to form a coalition.
The Socialists, whose term in government comes to an end in tandem with the departure of President Francois Hollande, have traditionally disputed power with the centre-right in France over the past half century. In interviews Monday, party officials said a new name would aim to broaden its appeal.
Whatever Le Pen's defeat means for populism's long-term future, Macron's victory can not disguise the fact that France remains a deeply-riven society on a number of issues and those divisions are not going to go away anytime soon.
The Republicans, Le Pen's National Front and Socialists all held meetings today to discuss strategy.
Macron won the presidency on Sunday and his new party has begun picking candidates for the June vote.
The two mainstream parties - the Socialists and the Republicans - are aiming to reassert themselves in the legislative elections, as is Le Pen's far-right National Front.More news: Vulnerable House Republicans distance themselves from Trump
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Sylvie Goulard, a centrist member of the European Parliament who supports Macron, told the CNews channel on Monday that Macron would go to Berlin for his first trip outside France, but she added that he might first visit French troops posted overseas.
The fervently pro-European Macron wants to team up with Germany to reform the European Union, which has been weakened by Britain's vote to leave.
Although every recent French presidential election has been followed by the winner's party going on to take control of parliament, the outcome this time around has been made murky by Macron's lack of an established base.
Berlin: Germany's Chancellor Angela Merkel on Monday congratulated Macron on his "spectacular" election success, pledging to help France tackle unemployment and to work together with him to promote European stability. However, he said the party would not be putting a candidate up against him, thereby offering a better chance of victory to a man who could be useful to Macron in the future.
Macron's party changed its name from En Marche (On the move) to La Republique en Marche in preparation for the June elections.
He also appeared with president Francois Hollande at a solemn Second World War commemoration.
Now Macron faces not only the formidable task of identifying, without party backing, a prime minister and agency heads, but also the challenge of winning support from the majority of some 577 new national legislators.