Gigolo is to man as what is to woman?
Solution 1:
There might have been a word to match the definition, once upon a time.
The English took the word gigolo from the French in the 1920s.
But the word was rather recent in the French language at the time. It had appeared in French, together with its feminine equivalent gigolette, in the middle of the 19th century.
What’s interesting is that there are two suspected origins to the words gigolo and gigolette in French. One of them is that both words derive from the Old English word giglet or giglot, which the OED defines as:
† a. Originally, a lewd, wanton woman (obs.).
b. A giddy, laughing, romping girl.
Solution 2:
There is "mistress".
7.
A woman other than his wife with whom a man has a long-lasting sexual relationship. [OED]
Also "kept woman".
Solution 3:
I believe it would be "kept woman". Take a look at the definition at Cambridge Dictionary Online:
someone who does not work but is instead given money and a place to live by the person she or he is having a sexual relationship with
It seems to be the closest parallel for a female gigolo. Mistress, on the other hand, does not necessarily receives financial support, even if it may be common.
Solution 4:
You might consider concubine, courtesan, or even châtelaine more suitable for a longtime paramour than the simple harlot or streetwalker implies.