Hamon, who is often compared to British Labour leader Jeremy Corbyn, is favorite to beat Valls in the primary's head-to-head vote, but has little chance of winning the presidential race proper after five years of unpopular Socialist rule.
Opinion polls have shown neither men would garner enough support to reach the election's runoff in May, and were likely to come in a humiliating fifth place in the first round behind centrist Emmanuel Macron and left-winger Jean-Luc Melenchon.
The two frontrunners are conservative Francois Fillon, currently embroiled in a scandal over his wife's work as his parliamentary assistant, and far-right leader Marine Le Pen.
But although the Socialist candidate has little chance of succeeding President Francois Hollande at the Elysee palace, the winner of Sunday's vote will help decide the fortune of other candidates.
A victory by Hamon, who wants to give a "universal income" to all citizens at a cost of 350 billion euros and tax robots, would boost Macron's chances by pushing Valls' center-left supporters into the former investment banker's arms.
Hamon, a former education minister, was kicked out of Valls' government in 2014 for differences on economic policy.
Macron was Valls' economy minister until he quit last year to launch his presidential campaign.
But he was not a party member, and has spurned the Socialist primaries that Valls and Hamon are contesting, having launched his own centrist political movement.
The latest polls show him breathing down the necks of Fillon and Le Pen. A Hamon win would also accelerate an influx of moderate Socialist lawmakers towards Macron, party members have told Reuters on condition of anonymity.
This refusal of the most pro-business wing of the party to rally behind a more radical leftist could hasten a break-up of the Socialist party, for decades one of the main political forces in France, analysts said.
"We now know these two different Lefts cannot govern together," Gerard Grunberg, a researcher and specialist of the Left at Sciences-Po university in Paris told France Info radio.
"It will be harder than ever before to cohabit. Which is why, it's true, we can say they have become irreconcilable."