Onetime frontrunner has been mired in scandal over allegedly paying his wife for a no-show job.
If the former prime minister prevails over Alain Juppe, he will face National Front's Marine Le Pen and a Socialist candidate.
A runoff is expected between Francois Fillon and Alain Juppe for the right to face the National Front's Marine Le Pen in the presidential election in 2017.
Alain Juppe is the favorite, with former president Nicolas Sarkozy and Francois Fillon also vying to face National Front leader Marine Le Pen.
The first round of voting in the presidential primary will take place Sunday.
Alain Juppe and Nicolas Sarkozy are the leading contenders for the Les Republicains' nomination for president.