The three activists - Yassir Hammoud, Barnabé Louche and Salem Aounit - filed a case on 12 May, basing it on party rules that say that the presidential candidate must be chosen by a primary "open to all citizens who adhere to the values of the Republic" to be held "at least one year before the presidential election".
The first round of France's next presidential election is to be held 23 April 2017 and, although the Socialists' national executive voted for a primary of all the left and ecologists on 9 April, it has not yet been held and no date has been announced for it.
The trio say they have contacted party national secretary Jean-Christophe Cambadélis on several occasions and had warned him that they would take the matter to court but have been greeted by "repeated silence".
The party's lawyer, Yves Baudelot, says that the question is on the agenda for the next executive on 18 June.
Divisions on the left
Although nobody opposes the principal of a primary, Hollande's supporters argue that the sitting president should be the only candidate.
That is not the view of Socialist rebels who believe the government has moved too far to the right, for example with its planned labour reform which has brought into conflict with unions and youth.
One, former economy minister Arnaud Montebourg, has hinted that he might stand.
Further to the left, Jean-Muc Mélenchon, who stood in the 2012 election, has declared he will stand again and held a rally of supporters on Sunday afternoon, as have representatives of two small Trotskyist groups.
The ecologists have voted against a primary with the Socialists and the Communist Party have said they will not support Hollande, whether there is one or not.
Hollande out in first round?
All is not harmony in the government, either.
Prime Minister Manuel Valls is widely believed to have presidential ambitions, although he seems to be restraining them this time round, and Economy Minister Emmanuel Macron has just launched his own "movement", En Marche (On the march), a decision that did not go down too well with some of his colleagues.
An opinion poll published on 1 June showed the left as a whole at just 32 percent in the first round, 10 points lower than in 2002.
It gave Hollande a mere 14 percent - only two points higher than Mélenchon - which would squeeze him out of the second round, leaving a mainstream right candidate facing off against the far right's Marine Le Pen.