Latin (and to some extent Greek) used to be the lingua franca during the middle ages.  Later on, French became the language of diplomacy and nobility.  Everyone that mattered \[1] speaks a local variation of said language which should still be understandable by another speaker.  For example, Quebecois and French or American and English.  

So, you could have such a language that all the PCs speak. They should be able to interact with everyone else.  Now, make sure that each PC speaks the language from where they will go adventuring.  If not, they will have to find a teacher and learn the language.  This does not take that much time.  You can learn everyday grammar and vocabulary in about three to six months of (hard) study.  This is what I do for all my games.

Well, almost all my games.  If the game is set in a bounded location, then only those languages that are around said location will be relevant.  If I set a game in 14th century Venice, I do not need to worry about the PCs speaking Japanese.  If I set a game in the Crusades, you better believe that everyone will learn Latin, French, and Arabic pretty damned quickly if they want to get anything done. 

If you have boogly powers (aka magic or psyonics or whatever), then learning languages could be done via it.  

As a side note, Middle Earth started as a setting to play with the evolution of different languages yet most characters manage to communicate quiet well -- and were delayed at the gates of Moria because of a translation error! 

**Philology is just cool.**  And just because it is hard to implement in game setting should not be a barrier to trying it out *provided that it enhances the enjoyment of the game*.

\[1] *Why, yes sire, I do have blue blood... What about Peasants? They don't need to speak to outsiders, they need to work harder and pay taxes.*