France's conservative UMP party, led by former President Nicolas Sarkozy, placed first in Sunday's local elections.
The UMP took 29 percent of the vote in Sunday's first-round election, while the FN received 25 percent.
Meanwhile, President Francois Hollande's ruling Socialist party trailed third with an estimated 22 percent.
National Front leader Marine Le Pen hailed the results as a "huge success."
The UMP and the Socialists will be able to call on allies when voters go to the polls in next Sunday's runoff election. Analysts say UMP and Socialist voters will likely switch allegiance in the runoff to whatever party will keep FN out of office.
Political observers say the FN, with its anti-immigration, anti-Islam and anti-euro platform, will be hard pressed to find allies.
Both the Socialists and the UMP, who are normally rivals, have issued warnings about France's future if the FN were to come to power.