As expected, 57-year-old former party leader Francois Hollande was in first place but, with most polling stations reporting, he had only 39 percent of the vote and was on course to face a tight run-off vote.
In next Sunday's second round, he will face 61-year-old Martine Aubry, a former labour minister best known for introducing France's 35-hour working week, who stood at 31 percent.
"I know that today I am ready to take on the challenges that confront our country. I am the candidate of change," Hollande declared, urging supporters of other candidates to rally behind him in the second round.
As Hollande noted, he was "clearly ahead", but his victory is not certain.
Next week, Aubry will hope to pick up many of the votes that went on Sunday to third-placed protectionist candidate Arnaud Montebourg, who surprised some observers by winning over many on the left of the party and scoring 17 percent.
"I'll beat Mr Sarkozy in 2012," Aubry said, arguing she is best placed to represent the desire for "change and renewal" revealed by the vote.
The night's big loser was Segolene Royal, Hollande's former partner and the mother of his four children, who was the defeated presidential candidate in 2007 and admitted it was "disappointing" to win only seven percent.
Behind her, from the right of the party, was free-market pragmatist Manuel Valls with about six percent. The only non-Socialist candidate, Jean-Michel Baylet of the Radical Party of the Left, won just one percent.
Montebourg did not endorse either of the frontrunners, Royale said she was considering her position and would make an announcement soon, and Valls called on his supporters to swing behind Hollande.
Hollande and Aubry have it all to play for in the last week of the campaign, but their party was already calling the vote itself a victory for the left, claiming a turnout in excess of two million.
"We've given a foretaste of the great French team that awaits us in 2012," Aubry said of rivals and comrades in the Socialist field, whose debate she said had given a good image of France and of politics.
Sunday's election was France's first ever US-style open primary open to any registered elector ready to pay a one euro fee and sign a declaration that he or she supports the ideals of the left.
"It's an immense victory for democracy, for citizens, for the French," said the party's interim leader Harlem Desir. "The Socialist Party is ready for its great appointment in 2012."
France has been led from the right since Socialist president Francois Mitterrand left office in 1995, and all recent opinion polls suggest that either Hollande or Aubry would defeat Sarkozy next year.
After five years in office, Sarkozy's popularity has been hit hard by the sputtering economy, high unemployment and a series of financial scandals.
Hollande benefited from the spectacular downfall of former IMF chief and Socialist presidential hopeful Dominique Strauss-Kahn, whose career ended when he was charged with the attempted rape of a New York hotel maid.
The US case against him collapsed, but Strauss-Kahn's long-planned campaign was sunk, and Hollande's equally careful preparation allowed him to fill the gap despite criticism that he lacks any ministerial experience.
Since last year, the former Socialist general secretary has been on the trail, meeting voters, losing 10 kilos of unpresidential body fat and shaking off an image as a jovial but uninspiring party apparatchik.
He has stuck to a cautious, centrist platform, arguing the left will lose credibility if it promises voters too much in a time of economic austerity and insisting he is best-placed to beat Sarkozy
This has allowed Aubry some room for manoeuvre to his left, despite the difficulties she has had persuading voters she is not a "substitute" candidate chosen by default after Strauss-Kahn dropped out of the running.
The primary was the climax of three months of campaigning enlivened by three televised debates between the candidates that were watched by millions.
"It's great to be able to choose the candidate of a party that you feel close to, it's a privilege -- at last we're taking the citizen into account," said one excited voter, 44-year-old Valerie Halin.
Sarkozy spent Sunday in Berlin discussing how to rescue European ailing banks with Germany's Chancellor Angela Merkel, but his supporters played down the significance of the primary and insisted the real race is next year.