There is no Common!
In many fantasy settings there exists a common language that is spoken or at least understood by everyone everywhere, often called just Common. Such a language does not exists in this world.
Most countries have their own language or languages and some countries share a common language. Like in the real world there are different language families, often common to specific geographical regions. Countries neighboring each other often have similarly sounding languages.
A few languages have gained a strong cultural influence and are being taught in schools in other countries. Similar to English in the real world. Still, just like in the real world, not everyone has a talent for languages and just because a language is taught in school it doesn’t guarantee that people will be able to speak it.
Another parallel to the real world is that the stronger languages in a region are often used in lyrics and poetry. Again, similar to English in the real world.
“Latin” the language of science
In the real world no one really speaks Latin these days (yes, I’m sure there are exceptions). Latin is however used a lot in the sciences, often for naming things. The same applies to this world.
It’s not actually Latin. It’s an old dead language that was commonly used in classical times and which is now used in the sciences (including wizardry) for naming purposes. For practical reasons translating it into a real world language results in something akin to a mix of Latin and Old Norse (I was gonna go with just Latin but Old Norse is cool too). I may try to come up with a different name for this language, something like Elder Classic or Nastlirn.
For fun and education I put a couple of English words through Google Translate. Check out the results here.
I’ll try to add my own versions of the translations as comments to this post as and when I make them up.
For now I’ve decided that the world Elves translates to the word Vaettir (from the Old Norse word Vættir).