"قِطّة اَلْمُهَنْدِس فَرَنْسِيّة."
Translation:The engineer's cat is French.
قِطّة اَلْمُهَنْدِس الفَرَنْسِيّ
The word French would become a attributive adjective (i.e. a part of the noun phrase "the French engineer"). It would have to agree in gender, number, case and definiteness with the noun it modifies. Here, the noun (the) engineer = اَلمُهَندِس is masculine, singular, genitive (it's not visible in this sentence, but it is genitive) and definite, so the adjective French = الفَرَنْسِيّ has to be masculine, singular, genitive and definite.
I reckon if it'd be "French cat", then "French" would be an attributive to cat, and since it's a defined cat (the engineer's cat), "French" has to be definite as well ie الفرنسة rather than only فرنسة
(This is what I thought to myself after getting the sentence wrong in the first place) Sorry about my grammar vocab lol x) I think AmineHadji1s explanation above is relevant too!