First, a small precision: The Gendarmerie Nationale is not exactly the French national police (called Police Nationale in French), but an armed force (the fourth french armed force, after infantery Armée de Terre, navy = Marine Nationale, air force = Armée de l'Air). The small difference between Gendarmerie & Police is that Gendarmerie members are exactly soldiers (with strict military discipline).
In practice, Gendarmerie tend to work in rural or semi-rural areas, while Police tend to work in urban zones (actually, there exist some kind of competition between Gendarmerie and Police, which gives interesting french thriller films and books) And they have different legal abilities. For example, in some limited cases, a Gendarme can legally shoot his gun first, while in principle a Policier (policeman) can use his gun (policemen and gendarmes are armed with guns) only for self defense (but IANAL so I may be wrong).
Gendarmerie is centralized and military, so it was easy to order them to switch at once to Linux [no training needed; just an official order from a high-rank official]. And I hear their IT department was strong enough to customize (without subcontractors) some Ubuntu distribution to the exact needs of Gendarmerie (which includes access to some peculiar databases). This could be an explanation of why Gendarmerie did not need any support from Mandriva.
But Mandriva still has several French state contracts, including even research contracts on collaborative projects.
Disclaimer: I do work sometimes with Mandriva on collaborative research projects (such as GGCC).