To expand on that question, what language did Christopher Columbus speak to them in when he had an audience with them? My understanding is that Columbus' native language would be some Genoese dialect of Ligurian, correct?
I would assume that Ferdinand's native tongue was Aragonese (or perhaps Catalan?) and Isabelle's would have been Castillian. What language would they speak to one another in? Did Ferdinand have a working knowledge of Castillian, did Isabella speak Aragonese or did they use another language as an intermediary, like Latin? Also, was Arabic ever used in the Catholic Monarch's court?
A reply to /u/TRexSparringPartner
By that point in history, the language of the Aragonese court and royalty was Castilian. It started at least in the reign of Ferdinand I Trastamara in 1412. By the time of Ferdinand II, the cortes of Aragon almost always met in Castile, such was the balance between the two realms.
Isabella was a stickler for the Castilian language. Nebrija the royal historian published a book of Castilian grammar in 1492, the first such compilation of a modern European language. "What is it for?" Isabella asked. The Bishop of Avila replied on Nebrija's behalf: "Your Majesty, language is the perfect instrument of empire."