TOG language headcanons part 2 (see here for part 1, oops all Andy edition)
Joe
I assume Yusuf spoke at least Arabic, a variety of Tamazight, and probably some amount of basic Greek before meeting Nicolò; how much of what else depends on the particulars of his backstory for any given fic.
Yusuf grew up bilingual, but in his youth he valued Arabic more because he saw it as the sophisticated and prestigious language of (written) poetry, literature, commerce, exotic foreign traders, etc., while Tamazight was just what the mostly illiterate folks outside the city spoke. He started to recognize the value of Tamazight more as an adult even before his first death, but he still regrets not having made more of an effort to preserve his native variety while he had the chance, because while there are still some related languages spoken in modern Tunisia, his variety effectively died out centuries ago.
Except for what he and Nicky still speak between the two of them. That is one of their most private and intimate ways of communicating because it is literally just theirs; Andy might be able to understand a bit here or there if she tried, but she mostly doesn't try because she knows anything they're saying in it is not for anyone else.
Joe does also speak a few of the modern Tamazight languages to varying extents and always has some complicated feelings about using them. It's a disquieting mix of familiarity and alienation, like walking into the place where some relatives that you visited often but were never that close to used to live, something that was never actually yours and is even less so now, but is still familiar in a way another stranger's house could never be.
With Arabic he doesn't feel as much of a distinction between what he grew up with and what people speak nowadays; he's aware that it's changed, but because he and Nicky have been speaking it with regular people at least as much as with each other over the centuries, his sort of 'default' way of speaking colloquial Arabic has evolved along the way. He'll still be thrown by new dialectal developments when returning to a place they haven't been for a while, but that's not really that different from dealing with a new dialect he's never encountered at all before.
He does tend to elicit a vaguely befuddled 'you're obviously a native speaker but where the hell are you from??' reaction from people with a good ear for accents pretty much anywhere in the Arabic-speaking world these days, because his way of speaking seems to be more Maghrebi than any of the other major dialect groups, but it doesn't actually match up with any particular modern dialect unless he's actively trying to speak a specific variety with the corresponding accent. Mostly he'll tell anyone who asks that his parents are from two different tiny villages with different obscure dialects somewhere that the asker has hopefully never been. When he does try to pass for A Normal Algerian or Egyptian or Syrian or whatever, it more or less works if they've spent enough time in that place recently, but if not he will eventually run into an actual Syrian who's like 'why do you sound like a mix of my auntie from Damascus, my grandpa from Aleppo, and the ancient literature I had to read in school??'
When it comes to other languages, I imagine he can pick them up relatively easily as needed and has a good ear for pronunciations; he's one of those people who will briefly peruse a tourist phrasebook before going on holiday in a place with a new-to-him local language, walk into a restaurant, greet the staff and ask for a table in said language, and then immediately have to start apologizing because they assumed he was a fluent if not native speaker and talked to him accordingly and he was lost three words in.
...and that is also a lot, so Nicky will go in part 3.