Socialist voters headed to polling stations from Sunday morning for the primary run-off vote between leftwinger Benoit Hamon and centrist ex-prime minister Manuel Valls.
Hamon, a 49-year-old former education minister, won the first round last weekend and has dominated the race with his radical proposals on work, state aid and the environment.
"Hamon brings principles on citizenship, solidarity and the sharing of wealth that are more the principles of the left," 60-year-old architect Annick Descamps told AFP as she voted in northwest Paris.
But Valls, 54, says his experience makes him a more credible choice and claims his rival's tax-and-spend programme would condemn the party to inevitable defeat.
Whoever wins is expected to face an uphill task with polls showing the Socialist candidate being eliminated in the first round of the election in April after five years of unpopular rule by Socialist President Francois
The contest is being watched closely after Britain's vote to leave the EU and Donald Trump's victory in the United States.
Polls currently suggest Fillon is most likely to win, ahead of far-right leader Marine Le Pen and independent centrist Emmanuel Macron.
The top two candidates from the April 23 first round will go through to the final vote on May 7.
But Fillon's campaign was embroiled in new controversy on Sunday, only days after reports his wife had been paid as a parliamentary aide without working.
The Socialist primary has confirmed a chasm within the ruling party, between a pragmatic, centre-left camp led by Valls and a staunchly leftist faction around Hamon.
Hamon won a first round of voting last week that whittled the candidates down from seven to two, taking 36 percent to Valls's 31.5 percent.
Around 7,500 polling stations opened at 0800 GMT, with voters able to cast their ballots until around 1800 GMT after paying one euro to participate.
"It's clear that Benoit Hamon goes into the second round of the Socialist primary in the role of favourite," Jerome Sainte-Marie from the polling group PollingVox told AFP.
One of the biggest potential winners of the primary could be former economy minister Macron.
The 39-year-old former investment banker, who quit the Socialist government last year to run for president as an independent, has been drawing large crowds at his rallies and is creeping up on Fillon and Le Pen in polls.
He is tipped for further gains if, as expected, Hamon beats Valls. Valls, a pro-business centrist who takes a tough line on law and order as well as Islam, has said he will not support Hamon's programme if the latter wins.
Hamon's ideas include a proposal to introduce a universal basic income to offset dwindling work opportunities in an age of automation. It would entail paying everyone, irrespective of income, a monthly stipend that would eventually reach 750 euros. Valls argues that would be the "ruin" of France.