Marine Le Pen's anti-immigrant, Eurosceptic party has led polling since President Emmanuel Macron called a surprise snap election in June that has plunged France into uncertainty and unnerved European neighbours and financial markets.
A new OpinionWay poll published by Les Echos newspaper on Friday showed the RN could reach as much as 37 per cent of the popular vote, up two percentage points on its score a week ago.
Macron's centrist bloc Together party was seen reaching 20 per cent, down by two points from the last publication.
The New Popular Front left-wing alliance stood at an unchanged 28 per cent of the vote.
The first round of parliamentary elections is on Sunday and the second round is on July 7. (AP PHOTO)
BFM TV, in a different poll compiled by Elabe, calculated the RN and allies could end up with 260-295 seats - potentially crossing the 289-seat bar for an absolute majority giving them a clear mandate to govern.
Accurate seat projections are tricky because the outcome depends on results in 577 constituencies.
Moreover, after Sunday's first round, rivals to the RN may team up and withdraw candidates in tactical moves to defeat far-right candidates in the second round on July 7.
An outright RN victory would position the party for an awkward "cohabitation" with Macron for the remainder of his term through to 2027, the first time a French president would have to share power with a party outside the political mainstream.
While the RN has toned down some of its anti-European Union positions and has vowed fiscal responsibility, questions remain over how it will fund its election promises and what its deep Euroscepticism will mean for EU integration.
Critics say racism underlies its "French first" policies despite Le Pen's efforts to detoxify a party inherited from her father Jean-Marie, who was convicted of inciting racial hatred.
The RN"s Jordan Bardella, left, and Prime Minister Gabriel Attal, centre, clashed over hate speech. (AP PHOTO)
In a final TV debate on Thursday, Macron's Prime Minister Gabriel Attal accused his RN challenger Jordan Bardella of continuing to tolerate racist speech in the ranks of his far-right camp - an accusation Bardella rejected.
The party has benefited from anger at Macron, whose decision to run as president back in 2017 at the head of a newly formed, broad-based centrist movement has reshaped French politics and was intended to counter the rise of extremist parties.
His rule has been credited with pro-business reforms but is perceived by many French voters to have ignored their concerns about the rising cost of living and weaker public services.
Le Pen gave a foretaste of the type of clashes that a cohabitation could trigger on Friday when she said an RN prime minister would veto Macron's preferred choice to serve as the French official in the European Commission in Brussels.
"It's the prerogative of the prime minister, not the president, to name the French commissioner," she told Europe 1 radio.
