Arnaud Montebourg, who scored a surprising 17 percent in Sunday's first round on a platform of protectionism and market regulation, told Le Monde newspaper that Hollande was best placed to win next year's presidential vote.
"I want the left to win and to defeat (President) Nicolas Sarkozy," Montebourg said.
"So, as a purely personal choice, I will vote for Francois Hollande, who was ahead in the first round and who in my eyes is the best unifier."
But Montebourg said he would not give his supporters "instructions on who to vote for," saying: "Each of my friends will make their choice according to their own conscience, and I will respect it."
Hollande, a 57-year-old former party leader and lawmaker, will face off with rival Martine Aubry, the 61-year-old mayor of the northern city of Lille, in a final primary vote on Sunday for the Socialist Party's nomination.
Hollande won the first round of the primary vote on Sunday with 39 percent, and had previously been endorsed by the three other defeated candidates, including his former partner, 2007 presidential candidate Segolene Royal.
Aubry came second with 30 percent but was expected to pick up many of the votes cast for Montebourg by appealing to the left-wing base of the party.
The run-off takes place at 10,000 polling stations across France and the stakes are high, with opinion polls suggesting either leading Socialist candidate would beat Sarkozy in next April's presidential election.
The primary itself -- the first time a French party has held a US-style open vote to choose a standard bearer -- has boosted the left, mobilising its base, dominating media coverage and drawing 2.7 million to the polls.