Seven candidates are competing to represent the Republican Party.
The forerunners include ex-President Nicolas Sarkozy and ex-Prime Ministers Alain Juppe and Francois Fillon.
The winner of the conservative primary seems assured to make the presidential run-off, where he or she is likely to face far-right leader Marine Le Pen.
Polls suggest that the Republican candidate would win that election. With the governing socialists unpopular and divided, it seems unlikely that any left-wing candidate will survive the first round,
The centre-right primary will be held in two rounds. The top two candidates in Sunday's vote will face each other in a second ballot a week later.
Voting is not restricted to party members. Those taking part have to sign a statement saying that they "share the Republican values of the right and the centre".
The candidates are:
People in France are due to take part in a US-style primary to chose a centre-right candidate who will run in next year's presidential election.