Indeed. Only converts were allowed to speak Arabic openly (and even then there were restrictions on the recently converted) so the spread of the language was very slow. Again, the Pact of Umar is an example of Dhimmitude and its origins are... contentious to say the least.

Latin would be the most logical choice, I think. It's no coincidence that the Holy Orders all spoke Latin as their main form of communication due to their universal nature of recruitment.