How would this be said in Latin?

All these quids & quods! "What language" is "quae lingua" or "quam linguam" according to case required.

The feminine accusative expressing "which" is not "quem" but "quam".

Quae haec lingua barbara est quam loqueris.

Quam linguam barbaram loqueris.

Nescio. Haec verba modo in mentem venerunt. Mirabile dictu!

(I don't know. These words just came to mind. Wonderful to relate!)

I am laughing so hard right now - I am glad zlevad answered before me, because I probably would have fallen into the quid trap myself. It is the interrogative pronoun, after all, and the first thing that comes to mind when a question starts with "what". But because of the linking verb, the interrogative adjective should be used, and it declines just like the relative pronoun. So he has given you the only grammatically corrrect answer.

The reason you have so many other different answers is because Latin has an extremely complex grammatical structure. The word ending changes depending on what gender, number, and case is being used. "Language" is feminine singular, and always nominative after a linking verb (as it is in English, although no one ever does). People always say "it is him", not "it is he". So it is easy for people to make that mistake in Latin, because we do it wrong in English - our native tongue, I might add. So you can see how hard it would be for people to translate correctly into a foreign language when our own spoken English is not grammatically correct.

In English, it is sometimes correct to omit a relative pronoun introducing a relative clause (what is this language THAT you are speaking) but it is always required in Latin. And since language is feminine, the word "that" must be feminine as well (quam, not quem, which is masculine).

No wonder the language broke down into the Romance languages - they have much simpler grammatical structures by comparison.

p.s. Vulgar Latin was just the common spoken language at the time, not the more formal style that is typically seen in written language. Not as much is known about it, as the Latin works that survive are mostly written works that were meant to be more formal. Note how we will say "bug" yet write "insect". Not all of the commonly used spoken words are known to us.

This is in classical. Because the sentence is simple, it may be no different from Vulgar, but I'm not positive:

Quid est hanc linguam peregrinam loqueris?

"peregrinam" means strange as in foreign, exotic.

"ignotam" means strange as in unknown, if you want to use that.

Now, if you want a nasty tone:

Quid est istam linguam barbaram loqueris?

CAROLINA: Not bad! You just forgot to match case and gender. (Do you feel like you're back in class? :-))

Carolina isn't the only one who forgot to match case. Try "Quid est haec lingua barbara [or peregrina] quem loqueris?" "Quem" ("which," which can't be omitted or just understood in Latin) is the only word in that sentence that should be in the accusative, because it's the object of "loqueris" ("speak"). "[H]aec lingua barbara" is a predicate noun and should be in the nominative case.

Qui est hic linguam barbarum dicis?

I agree to Aida