The LREM party won 32.32 percent of all votes, according to official final results published by the French Interior Ministry, in an election that was also marked by a record-high abstention of 51.29 percent.
If no candidate manages to achieve that target, then all candidates who won at least 12.5% of registered voters go to the second round, where the victor will advance to Parliament.
Between 7 and 12 MP seats are forecast to go to other political parties.
She pointed to the fact that only around 49 percent of the electorate cast a ballot on Sunday - the lowest level in a parliamentary election in France for six decades.
A comprehensive victory for Macron's party is largely seen as a market-friendly event, although the CAC 40 index was down nearly 1% on Monday at midday.
The centre-right Republicans had 21.5 per cent, while the far-right National Front (FN) had 13.2 per cent, followed by the far-left France Unbowed on just over 11 per cent.
The worst losses, however, were for the Socialists of Macron's deeply unpopular predecessor Francois Hollande, who are predicted to lose around 200 seats - a historic rout that has thrown the party's future into question.
The figures did not include votes from France's biggest cities and such early counts tend to be less precise than pollsters' estimates, which put Macron's party close to 33 percent.
Two parties, Le Pen's National Front and the small centrist MoDem party, an REM ally, are meanwhile under investigation over alleged expenses fraud at the European Parliament.More news: Brexit talks to begin amid post-election fallout in Britain
Polls suggest the elections will strongly favor Macron's party and dramatically shake up French politics, punishing the traditional left and right parties and leaving no single strong opposition force.
The biggest loser of the night was the Socialist party, which saw its support plummet, prompting talk of carnage and massacre.
According to the Ipsos/Sopra Steria projection, the conservative Republicans and their allies will get between 70 and 110 MP seats after the second round.
François Baroin, who ran the campaign of conservative party The Republicans, echoed these sentiments, saying political power should not be concentrated in the hands of one party and urging supporters to turn out on 18 June for the decisive second round. He voted for Macron's party, then brought his kids to play in the fountains of a Paris park on an extraordinary spring day.
It will be contested in next Sunday's second round by Mounir Mahjoubi, the youngest minister in Macron's new government, and hard-left candidate Sarah Legrain. Madani Cheurfa, secretary general of the Sciences Po CEVIPOF research institute, said in an interview that the legislative elections "will indicate what will be the practice of power for the next five years to come in France".
The elections also mark another low point for former rulers the Socialist party.
Macron, who won the presidency on his platform of being a pro-European centrist, is hoping to carry out far-reaching reforms in order to overhaul the country's political system and economy.
Speaking from the far-right stronghold of Henin-Beaumont in northern France, Le Pen, trying for the fourth time to win a seat in parliament, said she is well ahead in the constituency where she is running "more than 45 percent".