“France is back,” Edouard Philippe, the prime minister for Mr. Macron, said after the strong vote for the president’s party, though he lamented the relatively light turnout, about 49 percent of the voting public, according to the Interior Ministry.

“Despite the abstention, the message of the French has no ambiguity: For the third consecutive time, millions of you confirmed your attachment to the president of the republic’s project to renew, unite and win back,” said Mr. Philippe, whom Mr. Macron brought in from the mainstream, right-leaning Republican Party.

Those candidates garnering 50 percent or more of the votes in their districts will be declared the winners. But given the large number of candidates for each seat, and the low turnout, most of the top vote getters will face a runoff next Sunday. To claim a majority in Parliament, candidates supporting Mr. Macron will need to win at least 289 seats. Failing that, he has formed an alliance with the centrist Democratic Movement to help ensure a majority. However, as things now stand, it appears all but certain that the president will have a majority — and potentially a large one.

Parties on the extreme right and left seemed to be faring poorly, gaining far fewer votes nationwide than they had in the first round of the presidential election, on April 23. Returns showed that the National Front would take about 13.5 percent of the vote, while Jean-Luc Mélenchon’s leftist France Unbowed Party was expected to win just 11 percent.

At the same time, the traditional parties on the left and the right have been weakened, with the Socialists looking particularly feeble. Having controlled Parliament for the last five years, the Socialists were expected to win just 7.4 percent of the vote in the legislative elections this year. The Republicans and their allies fared better, but with just shy of 22 percent of the vote, they were a distant second to Mr. Macron’s party.