Such an outcome could plunge the country into a chaotic hung parliament, severely denting the authority of President Emmanuel Macron. Equally, if the nationalist, eurosceptic RN did win a majority, the pro-business, pro-Europe president could find himself forced into a difficult "cohabitation".
Marine Le Pen's RN scored historic gains to win last Sunday's first-round vote, raising the spectre of France's first far-right government since World War II.
But after centrist and leftist parties joined forces over the past week in a bid to forge an anti-RN barricade, Le Pen's hopes of the RN winning an absolute majority in the 577-seat National Assembly seem less certain.
Polls suggest the RN will become the dominant legislative force, but fail to reach the 289-seat majority that Le Pen and her 28-year-old protege Jordan Bardella believe would allow them to claim the prime minister's job and drag France sharply right.
Polls open at 4pm AEST Sunday and close at 4am Monday AEST in towns and small cities and 6am AEST in larger cities, with initial projections expected the moment voting ends.
President Emmanuel Macron has made a big gamble calling snap parliamentary elections. (AP PHOTO)
A longtime pariah for many due to its history of racism and antisemitism, the RN has increased its support on the back of voter anger at Macron, straitened household budgets and immigration concerns.
"French people have a real desire for change," Le Pen told TF1 TV, adding that she was "very confident" of securing a parliamentary majority.
Even if the RN falls short, it looks set to more than double the 89 seats it won in the 2022 legislative vote, and become the dominant player in an unruly hung parliament that will make France hard to govern.
Such an outcome would risk policy paralysis until Macron's presidency ends in 2027, when Le Pen is expected to launch her fourth bid for France's top job.
Macron stunned the country and angered many of his political allies and supporters when he called the snap election after a humbling by the RN in last month's European parliamentary vote, hoping to wrong-foot his rivals in a legislative election.
Whatever the final result, his political agenda now appears dead, three years before the end of his presidency.
Bardella says the RN would decline to form a government if it doesn't win a majority, although Le Pen has said it might try if it falls just short.
Prime Minister Gabriel Attal, who looks likely to lose his job in the post-election shake-up, has dismissed suggestions Macron's centrists could seek to form a cross-party government in the event of a hung parliament.
An RN-led government would raise major questions over where the European Union is headed given France's powerful role in the bloc, although EU laws are almost certain to restrict its plans to crack down on immigration.
The first round of the election resulted in the National Rally winning 33 per cent of the vote. (AP PHOTO)
For many in France's immigrant and minority communities, the RN's ascent has already sent a clear and unwelcoming message.
"They hate Muslims, they hate Islam," said 20-year-old cinema student Selma Bouziane, at a market in Goussainville, a town near Paris. "They see Islam as a scapegoat for all of France's problems. So it's bound to be negative for the Muslim community."
The RN pledges to reduce immigration, loosen legislation to expel illegal migrants and tighten rules around family reunification.
Meanwhile, voters in France's overseas territories and living abroad have started casting ballots. Voting began on Saturday off the Canadian coast in the North Atlantic territory of Saint-Pierre-et-Miquelon, and follows in French territories in the Caribbean, South Pacific and the Indian Ocean, along with French voters living abroad.
Reuters
