Both the Republicans - who had hoped to upstage Macron in the parliamentary election - and the Socialists of Macron's predecessor Francois Hollande looked set for steep losses.
Official final results released early Monday showed Macron s one-year-old REM and MoDem winning 32.32 percent in the first round, ahead of the Republicans on 21.56 percent and the FN on 13.20 percent.
That would put La Republique en Marche (LREM) within reach of an overwhelming majority in the National Assembly, with between 400 and 440 seats in the 577-seat lower house.
French far-left leader Jean-Luc Melenchon has decried the low participation rate in the first round of parliamentary elections, saying it shows France's volatile political situation.
Macron called on French voters to give him a "majority to make changes" on the night of his victory May 7.
The second round of the vote is held next Sunday.
President Emmanuel Macron's fledgling party is set to trounce France's traditional main parties in a parliamentary election and secure a huge majority to push through his pro-business reforms, projections after the first round showed on Sunday.
"France is back", Prime Minister Edouard Philippe declared triumphantly.More news: Do not disturb while driving feature for iPhone welcomed by Brake
Philippe said voters sent a "message without ambiguity" in the first round elections Sunday that they want a parliament with a "new face".
The prime minister also thanked security services for protecting voting stations and ensuring a safe vote after a string of deadly extremist attacks.
Meanwhile, far right leader Marine Le Pen, who lost to Macron in the presidential race, is on track to win a seat in the French parliament for the first time.
The Socialist Party that held power in the last legislature and its allies were all but vaporized - their 314 seats likely reduced, according to pollsters' projections, to as few as 20 seats, and possibly no more than 30, in the new assembly. Le Pen complained that the legislative voting system didn't fully represent voters' wishes - because her party got around 14 percent of votes but wasn't able to greatly improve on the two legislators it had in the last legislature.
Mounir Mahjoubi, junior minister in charge of digital affairs, said on BFM television that voters have acknowledged that the first weeks of Mr Macron's presidency "have been exemplary" and "have allowed the French to see there is a path that suits them".
Mahjoubi himself is running for a seat in Paris as a candidate with Macron's Republic on the Move party. The National Front party can receive from five to 15 seats in the parliament.
The move appears to have paid off as Macron's party, which has grown out of his grass-roots movement, is projected to record a stunning victory.
Only candidates who win more than 50 percent of the vote will take their seats, otherwise all candidates who secure at least 12.5 percent of registered voters will go into the second round to determine the victor. The Republicans and Socialists dominated the house for generations. Less than 50 percent of the 47.5 million electors cast ballots - showing that Macron has limited appeal to many voters. Top vote-getters advance to the decisive second round June 18.