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 Two.
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 protégé Jordan Bardella believe would allow them to claim the prime minister's job and drag France sharply rightward.
Polls open at 8 a.m. (0600 GMT) and close at 6 p.m. in towns and small cities and 8 p.m. (1800 GMT) in larger cities, with initial projections expected the moment voting ends, based on partial counts from a sample of polling stations.
Much will depend on whether voters follow the calls of leading anti-RN alliances to block the far right from power, or support far-right contenders.
Raphael Glucksmann, a member of the European Parliament who led France's leftist ticket in last month's European vote, said he viewed Sunday's run-off as a simple referendum on whether "the Le Pen family takes over this country."
"France is on the cliff-edge and we don't know if we're going to jump," he told France Inter radio last week.
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 on Wednesday, 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.
WHAT NEXT FOR MACRON?
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 shakeup, has dismissed suggestions Macron's centrists could seek to form a cross-party government in the event of a hung parliament. Instead, he would like moderates to pass legislation on a case-by-case basis.
An RN majority would force Macron into an awkward "cohabitation" with Bardella as prime minister, with thorny constitutional tussles and questions on the international stage about who really speaks for France.
If the RN is deprived of a majority and declines to form a government, modern-day France would find itself in uncharted territory. Coalition building would be difficult for any of the blocs given the policy differences between them.
French assets have risen on expectations the RN won't win a majority, with banking shares up and the risk premium investors demand to hold French debt narrowing. Economists question whether the RN's hefty spending plans are fully funded.
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.
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. Le Pen says she is not anti-Islam but that immigration is out of control and too many people take advantage of France's welfare system and creaking public services.
