The "Gendarmerie" is a part of the military that operates police duties. Although the concept was originally French, you can find a similar thing in a a lot of continental european countries (the Carabinieri in Italy, the Guarda Nacional Republicana in Portugal, the Guardia Civil in Spain, Internal Troops/National Guard in Ukraine, ...).

In France, generally speaking, the Police National is in charges of cities and large metropolitan areas, and the Gendarmerie is seen in rural areas. They live in barracks, and are weird in that they answer both to the ministry of interior and to the ministry of defense.