"The question to me is not whether the left can win, the left must win," Valls told a press conference to launch his 50-page presidential programme in Paris on Tuesday.
Although opinion polls show Valls the likely winner of this month's centre-left primary, none show him making it to the second round of the presidential election in June.
Valls refused to apologise for the record of the government he led between 2012 until his resignation last month ahead of the primary.
But he also demanded the "right to inventiveness" and pitched some new ideas for France and for the European Union.
His key proposals were:
An EU-wide minimum wage of 60 percent of each country's median salary, to be agreed by volunteer countries if unanimity cannot be reached;
An EU taxation "corridor" , setting a lowest and highest rate, for companies;
A conference to "refound" the European project and protect Euopean citizens in an age of globalisation;
A pause in EU expansion and an end to plans for Turkey to join;
Defence spending to be two percent of GDP in 2025;
At minimum extra 1,000 police officers to be recruited every year;
10,000 new prison places;
A pay rise for teachers.
A 15-billion-euro emergency fund to tackle unexpected crises.
Peillon wants new deal EU-style
Peillon, a loyal ally of President François Hollande who, like Valls, has only recently announced he is standing, also laid heavy emphasis on Europe when launching his programme on Tuesday.
Among his key proposals were:
A European new deal, led by the Franco-German alliance;
A eurozone job-creation budget and a 1,000-billion-euro European investment fund;
A humanitarian corridor to take in refugees;
France to employ 8,000 more teachers and 4,000 researchers and engineers over five years to "win the battle of intelligence";
The reform of the government's controversial labour law to restore the primacy of industry-wide collective bargaining;
Reduce nuclear power by 50 percent by 2025;
Ban shale gas and oil production and phase out diesel by 2025.
Socialist rebels keep campaigning
Montebourg, who was economy minister, proposed a cut in an indirect tax, the CSG, for the low-paid ahead of a press conference on Wednesday to spell out his economic and social programme, while Hamon pushed the idea of a universal basic income, an idea currently being tested in Finland.
Le Pen slams Fillon, defends Russia
In a high-profile TV interview on Tuesday morning, National Front candidate Le Pen defended Russian President Vladimir Putin, commenting that he "puts his country's interests first" and declared that Moscow's annexation of Crimea was not illegal, claiming it was validated by the 2014 referendum that Ukraine refuses to recognise as legitimate.
Although she could find common ground with Fillon on Putin, Le Pen laid into Republicans candidate's proposal to slash public health insurance, commenting that it would mean "the only people who will continue to receive health care will be the rich and illegal immigrants".