With President François Hollande deciding not to stand, the Socialist Party and its allies have set about finding a candidate for the election, whose two rounds are in April and May.
Twenty-four people put their names forward but 17 failed to collect enough sponsors.
One, left-wing national executive member Gérard Filoche, says he will challenge his exclusion.
The seven who have made it through are:
Manuel Valls, 54, resigned as prime minister to stand; on the right of the party, he will defend the government's record but also hopes to win over some of its critics, hence his surprise promise this week to scrap article 49-3 of the constitution, a measure allowing governments to pass legislation without parliamentary approval that his government used six times;
Arnaud Montebourg, 54, resigned as economy minister in protest at austerity policies, advocates a "great alternative project for France" and claims he can rally all wings of the party;
Benoît Hamon, 49, leading left-wing rebel who resigned as education minister in protest at austerity policies; doing well in the polls, he hopes to come from behind to victory as François Fillon did in the right-wing primary;
Vincent Peillon, 56, former education minister who has been off the political scene for the last two years and surprised everyone with his candidacy; says he stands for "political ethics" and the defence of the government's record;
Jean-Luc Bennahmias, 62, the leader of the Democratic Front and the Union of Democrats and Ecologists, ex-national secretary of the Green party EELV, which he left because he found it had turned ultra-left, and ex-vice-president of the liberal Modem;
François Rugy, 43, vice-president of the National Assembly, left the EELV at the same time as Bennahmias and for the same reason, represents his Ecologist Party in the race;
Sylvia Pinel, 39, the only woman, former housing minister and president of the small, centrist Left Radical Party.
Three television debates will be broadcast before the primary vote on 22 and 29 January.
Organisers are expecting a lower turnout than in 2011, when 2.7 million took part, although more than four million voted in the mainstream right primary last month.
The winner will have an uphill task to be elected president with none of the candidates doing better than Fillon and the far right's Marine Le Pen in opinion polls at the moment.
They will face competition for centre and left-wing votes from former economy minister Emmanuel Macron, hard-left candidate Jean-Luc Mélenchon and two Trotskyists, Nathalie Arnaud and Philippe Poitou.