Paramour may be the word you're looking for although it can be used for either sex.
an illicit lover; a person with whom someone is having a romantic or
sexual relationship and especially a secret or improper relationship.
Her husband found a love letter from her paramour.
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tl;dr: So long as you are content with historical terms rather than merely contemporary ones, the precise word you are looking for is coquet.
Here’s why.
The OED says that a coquette is first:
1. A woman (more or less young), who uses arts to gain the admiration and affection of men, merely for the gratification of vanity or from a desire of conquest, and without any intention of responding to the feelings aroused; a woman who habitually trifles with the affections of men; a flirt. In early use the notion ranged widely from gallantry, wantonness, or immodesty, to pretty pertness.
Curiously, it also provides a later subsense:
c. male coquette: = coquet B 1
Where we learn that the sense B 1 of coquet is
B. sb. 1. A man who from vanity or selfish motives aims at making himself generally attractive to the other sex; a male flirt; a ‘lady-killer’.
Whence we learn of this curious etymology:
a. Fr. coquet, orig. sb., dim. of coq cock, in reference to the strutting gait and amorous characteristics of the cock; hence ‘a beau’, and in the fem. coquette ‘a belle’; also as adj. ‘forward, wanton, gallant’: cf. cock v.1, also cockish, cocky a., and cocket a., which is prob. the same word in an earlier stage of meaning. In later use, the adjective in English became inseparably blended with the attributive use of the sb., to which also it became entirely assimilated in sense. The sb. was, as in Fr., formerly used of both sexes, and in both spelt coquet; but in the 18th c. the
fem. became coquette after Fr., and the masculine became obsolete.
The pronunciations given for both are identical.
Best Answer
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: