"A gendarme appeared"

French Gendarmes
Creative Commons Attribution Share AlikeFrench Gendarmes - Credit: David Monniaux
In France, gendarmes are quite separate to the civilian police.  The Gendarmerie is a military organisation with policing responsibilities.

The civil National Police, under the jurisdiction of the Ministry of the Interior, holds primary responsibility for policing in cities and larger towns.  The military Gendarmarie polices smaller towns and villages, representing about half the population, as well as fulfilling more specialist functions such as maritime security and counter-terrorism. 

Since Lavaurette is a small town, it is policed by gendarmes.