Her defeat in May brought huge relief to European allies who had feared another populist upheaval to follow Britain's Brexit vote and Donald Trump's election as US president, and disappointment to the party faithful.
Macron has banned all REM candidates from employing family members if elected and they must not perform consultancy work while lawmakers.
France has a new Goliath in politics.
Major results of all available exit polls showed that LERM won up to 33.5 per cent of votes, ahead of the conservatives which collected between 20.8 per cent and 22 per cent, Xinhua news agency reported.
The near-final first-round tally pointed to a legislative majority so crushing that Mr Macron's rivals fretted that the 39-year-old president will be able to govern France nearly unopposed for his full five-year term.
His party fielded political novices in around 200 constituencies.
Marine Le Pen (C), leader of French far-right National Front (FN) party, reacts with supporters after polls closed for the first round of the French legislative elections in Henin-Beaumont, northern France, 11 June 2017. The Socialists, party of former president François Hollande, didn't even make 10 percent.
Reformist Mr Macron has pledged to strengthen European Union ties, stabilise public finances, and loosen strictures on business.
Projections by three pollsters of the final outcome, based on the first round, gave Macron's movement and allies between 390 and 445 of the national assembly's 577 seats - potentially the biggest majority since president Charles De Gaulle's conservatives won more than 80 percent of seats in 1968.
The right, which only a year ago had seen the presidential and parliamentary elections as "impossible to lose", also faces a disappointing result and could be on track for its worst parliamentary score in France's postwar Fifth Republic on Sunday.
They also blamed the long election cycle, with party primaries that started previous year before the two rounds of presidential and then legislative voting, for turning voters off.
François Baroin, head of the Republicans, said the low turnout testified to the "deep divisions in French society" and was "extremely worrying". One stunning upset was that of the socialist party leader to 33-year-old Mounir Mahjoubi, Macron's new digital affairs minister and the son of Moroccan immigrants.
Responding to the criticism, a senior party official of Macron's Republic on the Move (LREM) party said there would be no riding roughshod over alternative views.
During the first round, candidates who recorded less than 12.5 percent of the vote are eliminated.
"I prefer a small opposition", du Pique says, "It's important in a free country not to leave all the power to one man".
The En Marche! party was predicted to secure up to 425 of the 577 seats as the first voting round got under way yesterday.
Macron's En Marche party is projected to win a strong majority in the second round on 18 June. The National Front party can receive from five to 15 seats in the parliament.
Macron, who had never held elected office before becoming president, will also have succeeded in ushering in a younger and more diverse parliament with more women and ethnic minorities.
While Macron's party is confident, the more traditional parties are expected to struggle.