The point of the manga may be just that the language can't and won't be figured out. At least for now...
But let's think here for minute. How can one learn a language without any references? You'd need to know the translations of the words in your native language. There's a good reason to assume that the MC's language doesn't exist at all in this new world. Sure, you may pick up some words. But what about grammar? Spelling? Pronunciation? Phonetics? Etc. All the nitty and gritty stuff, the tiny intricacies. You name it
Say an alien civilization from 1000 lightyears came to Earth, how on earth would an average person like you and me be able to figure out they alien's language from scratch??
Or an example closer to home: Egyptian hieroglyphs. They were ONLY able to be translated because of the Rosetta stone. If anything, you should hope that such a thing exists in the world where the MC currently is.
So really... with all these obstacles, how the f*ck is the MC supposed to know such an unknown language (without some magical power or Rosetta stone)!? Wanna bet you can all figure it out if you were there?
But I will admit that the MC could at least try and stuggle to learn something. Still, not enough reason to drop it.