Capitalizing on a sense of outrage over the attacks, which left 130 dead in the worst attack on French soil since the Second World War, and anti-immigrant sentiment, party leader Marine Le Pen said that the results indicated that the FN was now "the first party of France," according to CNN affiliate France 2.
With almost all ballots counted, the FN were leading nationally, ahead of former President Nicolas Sarkozy's conservative Les Republicains party and President Francois Hollande's ruling Socialist party, which came a dismal third nationally.
A second round of voting, which will determine the final results, will be held December 13. Parties which garner more than 10% of the vote are eligible to participate in the second round.
The Socialists have withdrawn their candidates from two regions, Nord-Pas-de-Calais-Picardie and Provence-Alpes-Cote d'Azur, ahead of next Sunday's runoff vote, in an attempt to consolidate support behind Les Republicains candidates in an effort to keep FN out of power, reports Agence France-Presse.
By removing underperforming candidates from contention, the Socialists hope that their supporters will switch their votes to Sarkozy's party and block Le Pen's FN from winning in the key regions.
For his part, however, Sarkozy has said that his party wouldn't withdraw from races to help the Socialists beat FN candidates.
Rise to power?
While the anti-immigration, anti-Europe FN has never controlled a French region before, the popularity of its leader -- the daughter of founder Jean-Marie Le Pen -- and her niece, Marion Marechal-Le Pen, a young firebrand and rising star of the party -- is set to change this.
Both Le Pen and Marechal-Le Pen garnered more than 40% of the vote in their respective regions -- the same areas where the Socialist have withdrawn their candidates.
As the second round approaches, Le Pen appears set to take the huge northern region of Nord-Pas-de-Calais-Picardie after a strong showing Sunday. The region is an economically depressed area of some 6 million people that was formerly a heartland for Hollande's Socialist Party.
Marechal-Le Pen, her 25-year-old niece, is also expected to win control of the Socialist-run southern region of Provence-Alpes-Cote d'Azur, an area that includes the wealthy French Riviera.
Voting in shadow of Paris attacks
The elections are the first to be held in France under a state of emergency imposed in response to last month's deadly attacks by Islamist radicals in Paris.
ISIS claimed responsibility for the attacks. In response, Hollande vowed to destroy the terror group and set about strengthening international efforts to wage a military campaign targeting its territory in Syria and Iraq.
The rise of attacks by Islamist terrorists, combined with the migrant crisis that has seen hundreds of thousands of mostly Muslim immigrants cross into Europe, has fed support for the National Front's anti-immigration policies.
Marine Le Pen told CNN's Hala Gorani in the wake of the Paris atrocities that Europe's acceptance of migrants on such a scale was "crazy."
"I had also warned ... the authorities very clearly that there will be in these immigrants terrorists, who will infiltrate ... and that's exactly what has happened," she said.
"Given this kind of huge threat, which is literally a declaration of war to France, we cannot take the risk."
The National Front came in third after the second round of voting in the previous regional elections in 2010, and third in the most recent legislative elections in 2012
, earning the party two seats in the National Assembly.
In May last year, the party caused shockwaves when it came up top in France's European elections
with 25.41% of the vote -- enough to win 23 seats in the European Parliament.