France's far right won the first round of pivotal legislative elections on Sunday with the centrist forces of President Emmanuel Macron coming in only third behind the left after the highest turnout in over four decades, estimates said.

But it remained unclear if the far-right National Rally (RN) party of Marine Le Penn would win an absolute majority of seats in the new National Assembly lower house in the July 7 second round and allow her to claim claim the post of prime minister.

Macron had stunned the nation and baffled even some allies by calling snap polls after the RN trounced his centrist forces in European Parliament elections this month.

That gamble risks backfiring, with Macron's alliance now expected to win a far smaller minority contingent in parliament, making the president a far less powerful figure for the remaining three years of his term.

Projections from prominent French polling firms gave the RN 34.5 percent of the vote, compared to 28.5-29.1 percent for the left-wing New Popular Front alliance, and 20.5-21.5 percent for Macron's centrist camp.

The polling agencies projected this would give the RN a majority of seats in the 577-seat National Assembly after the second round and a possible absolute majority.

In a statement, Macron called for a "broad" alliance against the far right in the second round.

With the French facing their most polarising choices in recent history, turnout soared. The Elabe organisation projecting a final turnout of 67.5 percent, the highest participation in a regular format legislative election in France since 1981.

The final turnout in 2022 was just 47.5 percent.

The July 7 second round will see run-off votes take place in seats where there was no absolute majority, allowing the final composition of the National Assembly to take shape. (AFP)