"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.