Polling stations opened at 08:00 a.m. local time (0700 GMT) on Sunday and will close at 08:00 p.m. local time (1900 GMT), with about 44 million people eligible to vote.
Voters are choosing leaders for the Western European state’s 13 newly-redrawn regions, which have wide powers over local education, transport and economic development.
Sunday’s elections will be also followed by a run-off scheduled for December 13.
The regional elections are being held under a state of emergency that was declared following the recent terror attacks, claimed by Daesh Takfiri terrorist group in the French capital city of Paris. On November 13, assailants struck at least six different venues in and around Paris, leaving 130 people dead and over 350 others wounded.