Francois Hollande has taken a lead in counting after the French primary to decide the Socialist challenger in the April 2012 presidential election.
An estimate based on 1.4m votes cast suggests Mr Hollande has a lead of 57% to 43% for Martine Aubry.
Opinion polls suggest either could beat President Nicolas Sarkozy, who is expected to stand for re-election.
It is the first time voters have taken part in a US-style primary to decide the Socialist candidate.
Ms Aubry is expected to concede victory shortly, the BBC’s Hugh Schofield reports from Paris.
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