The term "concubine" is used in English to refer to many different relationships across many different civilizations over millenia. A concubine is just a position which is inferior to that of a "wife". Some places might make a distinction based on the social position of the woman, or based on the order in which she was married to the man. A woman might be a concubine in that she is inferior to the first wife, but she might be legally married to the man and therefore a wife (and would refer to the man as husband).
To answer your question though, the legal terms of "wife" and "husband" would probably not be used, no matter what area of the world you're looking at. The use of the word "men" in your example looks like just a generic term for someone in a non-marriage relationship. "Man" is probably the best term to use for the man here, since it is understood that there is a relationship, without the use of translations people may not understand, or modern terms which could cause people to make associations they shouldn't.