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The second vote on Friday, which comes amid bitter party rifts, pits former presidential candidate Segolene Royal against Lille Mayor Martine Aubry.
Leftist MEP Benoit Hamon is out of the race after coming third in Thursday's vote. None of the candidates gained the 50% needed to avoid a run-off vote.
The leadership issue is being decided by 233,000 party members.
The voting comes after last weekend's party congress - that was meant to back a single candidate - ended in disarray.
In the first round, Ms Royal gained 42.5% of the vote, Ms Aubry 34.7% and Mr Hamon 22.8%.
After the count, Mr Hamon - who is seen by some as being too far-left - urged those who had backed him to vote for Ms Aubry in the second round, the AFP news agency reports.
The party has been beset by infighting since France's last Socialist President Francois Mitterrand stepped down in 1995.
Tough job
The candidates are vying to replace outgoing chief Francois Hollande.
At their annual congress in Reims at the weekend, top party members failed to reach consensus on a new leader.
Ms Royal - who had won a pre-convention ballot with 29% of members' votes - accused her rivals of clinging to "outdated" ways after they refused to rally behind her leadership bid.
One of the candidates, Paris Mayor Bertrand Delanoe, even pulled out of the race to "avoid creating further confusion".
"The Socialist Party is gravely ill," Mr Delanoe said. He has urged party members to back Ms Aubry.
Ms Royal, defeated by Mr Sarkozy in last year's presidential elections, has been accused of seeking to transform the party into her own personal electoral machine, the BBC's Emma Jane Kirby in Paris says.
Ms Aubry, the architect of France's 35-hour week, is seen by many as being too old-fashioned, although she has the backing of Mr Delanoe, our correspondent says.
France's media has said the Socialists showed themselves at the Reims convention to be "ungovernable".
It is clear that whoever becomes the new leader of the opposition will have a tough job uniting party members to build a credible challenge to President Sarkozy's government, our correspondent says.
(BBC)
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