The glossy website (with Twitter and Facebook accounts, and downloadable info pack) has the details: anyone who is on the French electoral roll, and who will be eligible to vote in the presidential election (even if not quite of age at the moment) can vote if they pay a €1 administration fee and sign a declaration that says:
Je me reconnais dans les valeurs de la Gauche et de la République, dans le projet d’une société de liberté, d’égalité, de fraternité, de laïcité, de justice et de progrès solidaire.
(I feel at home within the values of the Left and the Republic, in the construction of a society of liberty, equality and brotherhood, of laicism, justice and progress in solidarity)
The primaries take place on 9th and 16th October (two rounds, like most French elections). Oddly, voting has to be in person at a large number of voting stations set up in town halls – postal and internet voting isn’t available.