Hard-left Socialist rebel Benoit Hamon is heading into France's left-wing presidential primary as a surprising favourite to beat the pro-business pragmatist Manuel Valls.
Mr Hamon finished top in the first round of the contest, which will realign France's unpredictable presidential campaign, with 36% of the votes.
He proposes a "determined and optimistic leftist alternative".
The left-winger's most talked-about proposal is a 750 euro (£637) "universal income" that would be gradually granted to all adults.
Mr Harmon is now backed by another left-wing candidate, Arnaud Montebourg, who was eliminated from the race with 17.5% of the votes.
Mr Valls, who came second with 31.4%, criticised Mr Hamon's "unrealistic" promises.
A former junior minister and briefly education minister, Mr Hamon left the government in 2014 and led a group of rebel Socialist MPs who opposed the government's economic policies.
He told a rally near Paris on Friday: "Yesterday's failed solutions have no reason to become successes tomorrow."
Ten French economists, including Thomas Piketty - author of the best-seller Capital In The Twenty-First Century - have published an article to argue that the universal income can be "relevant and innovative".
They wrote: "Properly conceived and detailed, the universal living income can be a key element for reshaping our social model."
Mr Valls has tried to capitalise on his experience as prime minister from 2014 to 2016, despite his association with unpopular president Francois Hollande.
Mr Valls promotes "authority and security" values with the country still under threat from potential terror attacks.
He said he represents a "credible left" seeking a balance between France's social model and reforms adapting the country to globalisation.
"I don't want to be the candidate of the taxes; I leave that to my adversary," Mr Valls said in a rally near Paris.
"I want to be the candidate of work value, of jobs, with a clear and serious roadmap offering a future to the French people."
The French Socialist party has been torn for years between advocates of a radical left, including Mr Hamon and Mr Montebourg, and others sharing centre-left views, like Mr Valls and Mr Hollande.
Divisions are so deep that if Mr Hamon wins on Sunday, some supporters of Mr Valls are expected to back centrist figure Emmanuel Macron, who is campaigning for president as an independent candidate.
However, early polls show that whatever the outcome of Sunday's vote, the Socialist nominee is currently ranking in fifth position in the race for the French presidency.
Far-right leader Marine Le Pen and conservative leader Francois Fillon appear to be far ahead, followed by Mr Macron and far-left figure Jean-Luc Melenchon.
Another sign of the Socialist party's struggle is that the first round was marred by irregularities in the vote count.
Results were not in dispute, but the number of voters was. Observers suspected organisers of trying to increase it artificially in order to give their future nominee more legitimacy.
In the end, the party announced 1.6 million voters last week. This compares to four million people who cast ballots at the conservative primary in November.
The primary is open to all voters who pay one euro and sign a document saying they share the left's values.