The winner, either Francois Fillon or Alain Juppe, will most likely represent the entire French political mainstream against the National Front's Marine Le Pen, in another test of the anti-establishment anger in Western countries that saw Britain vote to leave the EU and Americans elect Donald Trump as president, according to Reuters.
Opinion polls show Fillon, a social conservative with a deep attachment to France's Catholic roots, as the clear favorite after stunning his more centrist challenger with a surge in support just before the November 20 party nomination first round.
Voting opened at more than 10,000 polling stations across France at 8 a.m. and was set to close at 7 p.m., with the first results likely up to an hour and a half later, according to the report.
A 62-year-old racing car enthusiast who lives in a Loire valley chateau, Fillon promises radical reforms to France's regulation-encumbered economy, vowing to roll back the state and slash government's bloated costs.
Scrambling to regain momentum, Juppe, 71, a soft-mannered moderate who is now mayor of Bordeaux, has attacked the "brutality" of his rival's reform program and says the Paris lawmaker lacks credibility.
But in a blow to Juppe, television viewers found the harder-line Fillon more convincing in a head-to-head debate on Thursday, Reuters wrote.
Pollsters say the winner of the center-right primary will be the favorite to enter the Elysee palace, likely to place in the top two alongside Le Pen in a first round in April and defeat her in a run-off in May.
While polls show either Fillon or Juppe would beat Le Pen, Juppe would do so by a more comfortable margin. But the shock results in the British referendum and U.S. presidential contest mean forecasters' assumptions are being treated with caution.
