The body of a woman was found on Tuesday morning in a suburban street in Colombelles, east of Caen (Calvados).
She was reportedly killed with knives.
According to Ouest-France, the victim, aged about fifty, resided in the rue de la Fraternité.
Numerous police vehicles are on site to allow the investigations to proceed smoothly, including the collection of scientific evidence, and to interview residents.
According to the regional daily, a man in his thirties is in custody, after having himself contacted the police.