The anti-immigration and anti-EU party scores 24 percent in the Ifop survey, published in today’s left wing weekly Le Nouvel Observateur, which polled 1, 893 people on 4 October.
The results follow Sunday’s electoral success for the FN in a local by-election in the south, where it came top, garnering almost 50 per cent of the vote.
"For the first time in a poll on voting intentions in an election of a national character, the FN is clearly ahead of both the (ruling) Socialist Party and the UMP", the main centre-right opposition party, Ifop said.
The Front National led by Marine Le Pen has gained three percentage points since a similar survey conducted by Ifop in May.
At the 2009 EU-wide elections, when Nicolas Sarkozy was French president, Le Pen's party took only 6.34 percent of the vote.
In the new poll, Sarkozy’s centre-right UMP comes second after the FN, scoring 22 percent.
President Francois Hollande's Socialist party is in third place with 19 percent, a two percentage point drop over May.
Analysts say record unemployment, a struggling economy and mounting concern over crime have bolstered support for the FN.
Since taking over as the head in 2011, Marine Le Pen has tried to reposition the party whose image had long been closely linked to her father, Jean-Marie Le Pen, who had convictions for incitement to racial hatred and holocaust denial.
Under her leadership, the FN has expelled overtly racist activists and selected a number of ethnic minority candidates for local elections.