The National Rally party won a crushing victory in the first round of voting for the French National Assembly, according to early projections, bringing its long-taboo brand of nationalist and anti-immigrant politics to the threshold of power for the first time.

Pollster projections, which are normally reliable and are based on preliminary results, suggested the party would take about 34 percent of the vote, far ahead of President Emmanuel Macron’s centrist Renaissance party and its allies, which got about 21 percent.

The scores, in a two-round election that will be completed with a runoff on July 7 between the leading parties in each constituency, do not provide a reliable projection of the number of parliamentary seats each party will secure. But the National Rally now looks very likely to be the largest force in the lower house, although not necessarily with an absolute majority.

A coalition of left-wing parties, called the New Popular Front and ranging from the moderate socialists to the far-left France Unbowed, won about 29 percent of the vote, according to the projections. Turnout was very high, reflecting the importance accorded by voters to the snap election, at over 65 percent, compared to 47.51 percent in the first round of the last parliamentary election in 2022.

For Mr. Macron, now in his seventh year as president, the result represented a severe setback after he gambled that his party’s stinging defeat to the National Rally in the recent European Parliament election would not be repeated.

In a statement released immediately after the projections were released, Mr. Macron said that “confronted by the National Rally, it is time for a large, clearly democratic and republican alliance for the second round.”