The eventual winner of the primary is likely to go head-to-head with far-right leader Marine Le Pen for the French presidency
Former French president, Nicolas Sarkozy has conceded defeat in his bid to become the centre right candidate in the upcoming elections.
Sarkozy, who held the presidency between 2007 and 2012, had been lying third in yesterday’s US-style primary after more than 80% of the votes had been counted.
The 61-year-old told his supporters, "I failed to convince a majority of voters."
The two remaining candidates, Francois Fillon who was leading the count with 44.1% of public votes and Alain Juppe, who has so far secured 28.2% of the votes, will now go forward to a second round of voting.
Mr Fillon served as prime minister under Sarkozy, while Mr Juppe was prime minister from 1995 to 1997 under President Jacques Chirac.
It is expected that the pair will now face each other again on 27 November - unless Mr Fillon ends up with more than 50% of the vote when counting finishes later today.
Whoever wins that vote is likely to go head-to-head with far-right leader Marine Le Pen, who is predicted to be one of two in the final round of the French presidential election, next May.
The ruling Socialist party, under the current President Francois Hollande, is in disarray, with polls showing he is likely to be eliminated in early voting next year.
Ms Le Pen is campaigning on a pro-nationalist, anti-immigration ticket amid growing fear of Islamist terrorism.
Her rise has been attributed to the same sentiment that prompted Donald Trump's victory in the US and Brexit in the UK.
She has spoken of how the Brexit result and Trump's shock victory were signs of the "emergence of a new world" in which disillusionment with mainstream politics has led many in France to consider her their only hope.
For months, pollsters have been predicting Mr Juppe would win the primaries and subsequently defeat Ms Le Pen.
His second place will further cast doubt over whether the polls are able to correctly predict the outcome of the vote.
A number of analysts have put Mr Juppe as the most likely to be able to beat Ms Le Pen, if the pair were to face each other.
One analyst, Charles Lichfield of Eurasia Group, gives Ms Le Pen a 25% likelihood of beating Mr Juppe. However, he said if she goes up against Mr Fillon, her chances of winning may jump to 35%.
A number of European leaders have voiced their concern at the prospect of a Le Pen victory with Austrian Chancellor, Christian Kern claiming it could badly damage Europe’s economy.
Others have suggested a Le Pen presidency could lead to the break-up of the eurozone.