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.
A poll showed that only 52% of voters want a pro-Macron government to emerge from the elections, while 42% favoured a legislature that would be a check on the new leader.
Francis Kalifat, president of CRIF, called the victory "incontestable" and congratulated Macron on it.
In 2014, Macron became minister of economy, industry and digital data under President Francois Hollande.
Like the presidential race, France's legislative elections are split into two rounds. Everyone told us it was impossible.
"I am more than relieved, I am delighted to see that Emmanuel Macron has won the election by a wide margin", Catherine Cesarsky, an astrophysicist at the CEA, France's atomic energy commission, told Nature News. "He has stood up for liberal values; he put forward a vision for the important role that France plays in Europe and around the world; and he is committed to a better future for the French people". If another party wins a majority, Macron could be pressured to choose a prime minister from that party.
In an early plea for unity, Macron reached out to Le Pen's supporters after a vicious election campaign that exposed deep economic and social divisions, as well as tensions provoked by identity and immigration. A key aide said the party would change its name as part of a revamp. Several senior members of his Socialist Party have already announced plans to launch new movements, inspired by divisions in the party ranks and perhaps by Macron's success. The abstention rate was 25.44 per cent, the highest since the presidential election in 1969.
This could give the National Front a significant increase on the two seats the party now holds.
European Union leaders heaved a sigh of relief over Le Pen's defeat.
In a victory party on Sunday evening, Macron walked on to the stage to the strains of "Ode to Joy", the anthem of the EU.
The White House said in a statement the president "emphasized his desire to work closely with President-elect Macron in confronting shared challenges, and noted the long and robust history of cooperation between the United States and its oldest ally, France".