I have written before about strings of words borrowed from (and through) English in Korean: Maxim mocha gold mild coffee mix. It happens in English, too. Walking to the venue for dinner with colleagues last night, I saw TRUMPS ALTO EGO HOMMES FEMMES COIFFURE SPA, which contains no native English words (that is, attested in English before 900). Some of them have become (more) ‘English’ while others remain less so.
Card-game trump dates from the early 16th century and is derived from triumph, which is the most native word on the list, dating from before 900 but being derived from Latin triumphus, which in turn is possibly derived from Greek thríambos, a hymn to Dionysus. Literary/musical trump dates from the late 13th century is derived from Old High German trumpa or trumba. Trumpet is now standard English, but trump is still literary. (Note that trump entered English first.)
Alto ego is either an error or a deliberate play on alter ego. Google has 228,000 for the former (including this establishment) and 22,800,000 for the latter (rather suspiciously, a ratio of exactly 1:10). Either way alto, alter, ego and alter ego are all from Latin. Note that the phrase alter ego (another I) was used in English for several centuries before the psychological meaning of ego, and that the verb alter was used for several centuries before that. I assume that an alto ego is meant to be a higher self.
Hommes and femmes are pure French. How ‘English’ you regard them might affect whether (English) or not (French) you pronounce the final /z/. Femme (or fem) has developed a distinct meaning in English: a lesbian who is notably feminine in appearance. The owners might have used English mens’ and womens’, but using French gives it a certain je ne sais quoi.
Coiffure is also from French. Some English-isation is shown in the change of pronunciation: English kwah-fyoor v French kwa-fyr. (Note that coif (a hood-shaped cap) has been an English word since the late 13th century and has an English-ished pronunciation koif.)
Spa is from the Belgian town of the same name, which in turn is derived from Latin Aquae Spadanae, but there is uncertainty about the meaning of spadanae.
So the owners might have called it Triumphs (or trumpets) higher (or other) self mens’ and womens’ hairstyles and hot tubs, but that wouldn’t be anywhere near as chic.