The Ipsos survey - conducted for Le Parisien newspaper and Radio France on June 19-20 - showed the left-wing New Popular Front (NPF) alliance in second place with 29.5% of the vote, Reuters reported.
President Emmanuel Macron's centrist alliance was seen in third place, winning 19.5% of votes.
The turnout rate is seen at between 60 and 64%, which would be much higher than the 47.5% seen at the last general election in June 2022.
The RN's lead in polls ahead of the election that will take place in two rounds, on June 30 and July 7, is unlikely to win the party an absolute majority. Macron called the ballot after his alliance's crushing defeat at EU elections earlier this month.
In a separate Ipsos survey, published by the Financial Times, the National Rally is seen as the most trustworthy when it comes to managing the economy and public finances.
According to the survey, 25% of respondents trust Marine Le Pen's RN the most to take the right decisions on economic issues, versus 22% for the New Popular Front and 20% for Macron's alliance.