The RN was seen winning around 34% of the vote, exit polls from Ipsos, Ifop, OpinionWay and Elabe showed.
That was ahead of leftist and centrist rivals, including President Emmanuel Macron's Together alliance, whose bloc was seen winning 20.5%-23%. The New Popular Front (NFP), a hastily assembled left-wing coalition, was projected to win around 29% of the vote, the exit polls showed.
The exit polls were in line with opinion polls ahead of the election, but provided little clarity on whether the anti-immigrant, eurosceptic RN will be able to form a government to "cohabit" with the pro-EU Macron after next Sunday's run-off.