Projections show La République en Marche (Republic on the Move) and its MoDem ally set to win up to 445 seats in the 577-seat National Assembly.
The final outcome will be decided at a run-off next Sunday.
Mr Macron's party was established just over a year ago and many candidates have little or no political experience.
After disappointing results, traditional parties have urged voters to support the president's rivals in the second round, to avoid him monopolising power.
What are the results?
With all the ballots counted, Mr Macron's LREM and MoDem won 32.3% of the vote.
The centre-right Republicans had 21.5%, while the far-right National Front (FN) had 13.2%, followed by the far-left France Unbowed on just over 11%.
The Socialists, previously France's ruling party, and their allies won just 9.5%. Projections showed them losing up to 200 seats.
But turnout was sharply down, at 48.7% compared with 57.2% in the first round in 2012, which analysts said reflected a sense of resignation among Mr Macron's opponents.
Turnout was low, despite claims that President Macron had re-energised the voting public
Only four seats were settled on the first round. In the run-off vote next Sunday, the other seats will be disputed by the two top-placed contenders and any other candidate who won the support of at least 12.5% of registered voters in the district.
The election took place amid heightened security after a series of devastating terror attacks in recent years.
What has the reaction been?
François Baroin, head of the Republicans, said the low turnout testified to the "deep divisions in French society" and was "extremely worrying".
FN leader Marine Le Pen blamed her party's poor performance on the low turnout, saying France's electoral system, which favours larger parties, needed to be reformed.
FN leader Marine Le Pen said the electoral system led to low turnout
"This catastrophic abstention rate should raise the question of the voting rules which keep millions of our compatriots away from the polling stations," she said.
Socialist leader Jean-Christophe Cambadélis lost his seat in the first round.
He warned voters against giving LREM an absolute majority next Sunday, saying it would result in "virtually no real opposition and we will have a National Assembly without any real counterbalance, without a democratic debate and not worthy of that name".
Elsewhere, German Chancellor Angela Merkel - who, like Mr Macron, has a pro-EU stance - congratulated him on the "great success" of his party. It was a "vote for reforms", tweeted (in German) her spokesman, Steffen Seibert.
What are the challenges for Macron?
Mr Macron, 39, defeated Marine Le Pen in the presidential run-off last month.
He needs a majority to push through the changes that he promised in his campaign, which include:
- Budget savings of €60bn (£51bn; $65bn) in the next five years
- Cutting the number of public servants by 120,000
- Reforming the labour market and generous state pension schemes, bringing them into line with private schemes
He has already left an impression around the world, in particular for standing up to US leader Donald Trump on issues like climate change.
After the projections were announced, a government spokesman said voters had shown they wanted to move fast on major reforms.
Those standing for LREM come from all walks of life and include students, retired citizens and a bullfighter.