Concubinage

In French, the term that corresponds to a cohabiting couple, legally defined as a “union of fact, characterized by a shared life presenting a character of stability and continuity, between two persons, of different sexes or of the same sex, who live as a couple," is "concubinage" and a member of such a cohabiting couple is a "concubine." See French Civil Code, Article 515-8 (adopted in 1999). 

In France, government and HR forms which ask about your marital status frequently have four check the box choices which are: "married", "registered civil union member" a.k.a. PACS (including many opposite sex couples, even though this option was initially invented for same sex couples), "concubine" and "single."

By French reckoning, most of us are now concubines, or were formerly concubines.

The term (inflected for gender) had substantially the same meaning, without the modern English language connotations, in pre-Christian Rome, although it was most often used then for couples who were legally prohibited from marrying because they did not come from the same social class. 

Concubinage was actively vilified as Christianity became more common in the Roman Empire, acquired a negative connotation at that time, and was eventually banned. The term retained the negative connotations that it has in the English language in French, although never quite as strongly negative as they were in English (in which the term "concubine" is limited to women and implies a status only marginally better than "sex slave"), until roughly the 1960s, when the term came to acquire, in French, its more neutral and descriptive current connotation. 

This was the case until the 1960s, despite the fact that all of the daughters of Charlemagne (the legendary medieval king seen as the founder of the French nation) who became mothers were concubines and yet continued to participate in his court in good standing, despite the fact that none of Charlemagne's daughters married, and despite the fact that Charlemagne himself was a concubine (as the French currently define the term) for part of his life. In short, Christian influence on this aspect of French culture ca. 800 CE, was minimal, despite the fact that Charlemagne was a strong supporter of the Roman Catholic Church.