Opinion polls have shown strong support for Marine Le Pen's anti-immigration party, which has never controlled a French region.
That could be about to change, with National Front candidates ahead in polling in a number of the country's 13 regions.
Le Pen, the 47-year-old daughter of the party's founder, Jean-Marie Le Pen, appears set to take the huge northern region of Nord-Pas-de-Calais-Picardie, an economically depressed area of some 6 million people that was formerly a heartland for France's ruling Socialist Party.
Her 25-year-old niece Marion Marechal-Le Pen -- the party's rising star -- 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 that killed 130 people.
ISIS claimed responsibility for the attacks. In response, French President Francois 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 second round of voting, which will determine the final results, will take place on December 13.
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.