Voting has begun in France in one of the country’s most important elections in living memory, with the far-right National Rally (RN) of Marine Le Pen and its allies poised to become the dominant force in the national assembly.

Voting got under way across mainland France at 8am local time on Sunday, with pollsters due to publish usually reliable seat projections as the last big-city polling stations close at 8pm.

The “republican front” is thought likely to block the anti-immigration, Eurosceptic party from winning an outright majority of 289, with a final Ipsos poll indicating the RN and its allies would send between 175 and 205 deputies to the 577-seat parliament.

That would still give the RN a parliamentary party more than double the size of its 88-strong group in the outgoing parliament, however, with the number of MPs from the centrist coalition of the president, Emmanuel Macron, forecast to halve to at most 148.

The New Popular Front (NFP), a four-way left-wing alliance dominated by the radical left Unbowed France (LFI) of Jean-Luc Mélenchon, was expected to win between 145 and 175 seats, likely making it the second-largest force in the new assembly.

Macron, who called the snap election less than a month ago after his camp suffered a humiliating defeat at the hands of the RN in the European elections, looks set to face the final three years of his presidency with no clear ruling majority.