With the field now whittled down from seven candidates to two and Valls and Hamon set to meet mid-week for what could be a testy televised debate, the final outcome was hard to predict.
But former economy minister Arnaud Montebourg, who trailed in third place, gave Hamon, a party ally on the left, an advantage by criticizing Valls`s pro-business policies and urging his supporters to vote for Hamon next Sunday.
Either way, opinion polls indicate that no Socialist candidate has much chance of getting beyond the first round of the election in April-May after five years of unpopular rule by Hollande.
The Socialist party, for decades one of the main political forces in France, has become marginalized as Hollande failed to bring high unemployment down and alienated left-wing voters with his economic policies.
But the Socialists` final choice on January 29 could have an impact on the election fortunes of the front-runners for the Elysee - conservative Francois Fillon, far-right leader Marine Le Pen and popular independent Emmanuel Macron.
Polls indicate Fillon, a former prime minister who has The Republicans ticket, is most likely to win if he is pitted against National Front leader Le Pen in a May 7 head-to-head.
But Macron, a 39-year-old former banker and one-time economy minister who pushes a centrist agenda and tries to appeal to both left and Right is attracting large crowds to rallies and could yet upset the balance.
CENTER-GROUND BATTLE
The Spanish-born Valls, who implemented pro-business policies under Hollande to the conservation of the traditional left-wing, appeals to a more moderate electorate and will pose a greater challenge to Macron for the center ground.
Conversely, political commentators say a traditional Socialist such as Hamon, who wants to legalize cannabis and establish a basic state income level of 600 euros per month for all adults, will benefit Macron in his campaign.
"I can see the first bricks with which we can reconstruct the left and reunite the left and then also rebuild hope and share this with the people of France," Hamon said in a short address to his supporters after the result.
Valls, 54, in combative mood, suggested that Hamon stood no chance of pulling off victory in spring and that he alone would be able to turn the tide against the odds.
"We face a choice now between certain defeat and possible victory, between unrealistic promises that cannot be financed and a credible left that can bear responsibilities," Valls said, referring to Hamon`s proposal on basic income.
Partial results showed that with half the vote counted, Hamon had won 35.2 percent and Valls about 31 percent. Montebourg had about 18 percent.
Calling on his supporters to vote for Hamon next Sunday, Montebourg said: "Voters massively and seriously rejected those who carried out free-market, austerity policies during the presidential term."
Hamon and Montebourg were kicked out of Valls`s government in 2014 for criticizing economic policies which they said were too business-friendly.
The program of Fillon, seen as the election front-runner, includes cutting business taxes, relaxing labor laws and scrapping the 35-hour working week in an attempt to boost growth, while also eliminating half a million public sector jobs as part of a drive to shrink the state sector.
Anyone who pledged allegiance to the political values of the left and paid a one euro fee were able to vote in the primary. Organizers of the primary said there had been a turnout close to two million.
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