As polls closed, projections showed La Republique en Marche (Republic on the Move) set to win more than 400 seats in the 577-seat National Assembly.
Mr Macron's party was established just over a year ago and many candidates have little or no political experience.
The second round of the vote is held next Sunday.
Forecasts by two polling organisations gave LREM well over 30 percent of first round votes.
But turnout was low, about 49 percent, which analysts said reflected a sense of resignation among Mr Macron's opponents.