About 44 million people are eligible to vote in the first poll since the Paris attacks, which killed 130 people.
The far-right National Front (FN) is hoping to make gains, while the centre-right Les Republicains party, led by former President Nicolas Sarkozy, is expected to win a majority of regions.
The FN leader, Marine Le Pen, is likely to win in the northern region, while her niece, Marion Marechal-Le Pen, is a leading contender in the southern region of Provence-Alpes-Cote d’Azur.
Prime Minister, Manuel Valls, on Thursday made an “appeal to patriotism” in an effort to rally the socialist votes.
The second round is on December 13.