The Civil Code of France 2009, §515-8, defines concubinage as follows:
"Concubinage is an union in fact, characterized by a life in common offering a character of stability and continuity, between two persons, of different sexes or of the same sex, who live in couple."
This is the French civil law system's equivalent to what the common law would refer to as a common law relationship or cohabitation relationship.
Also, in French, l'union de fait.