D&D has rarely handled languages well. In some campaigns, you have multiple languages for the same species- maybe there's a High Elvish or an Old Common (Ed Greenwood's Thorassic Script, which shows up in old ruins). Perhaps there's a High Common reserved for court and diplomatic functions as part of tradition.
I mean we have Undercommon, so the idea of another lingua franca isn't ridiculous. Asian-inspired settings often simply call these Trade Languages (which is what they are, certainly). In my games, Drow typically have to know three languages (Undercommon, Elvish (it's true there are linguistic changes from what the other Elves speak, but I figure Drow and surface Elves can communicate with one another), and Drow Sign Language (jokingly called DSL by some of my players). And many know Common as well!
Sometimes D&D gets pretty deep into this, and characters might find that they don't have enough languages to cover their needs. Other times, knowing how to speak, say, Celestial, may never come up at all. And that's not getting into "secret" languages like Cant, Druidic, or Lawful Neutral.
I've never really known how to handle this. I could easily give my D&D games a bewildering array of languages (ie, closer to the real world) or even "six million forms of communication", but I have doubts that the juice would be worth the squeeze.
I've played a few adventures where you encounter "an unknown language" and it's supposed to be this big deal, but generally either the adventure provides the means for you to learn how to read/speak it, or the DM just sighs when the players use spells, magic items, or conjured Word Archons to handle it for them (which happened in the Midgard game I'm playing in- but by the end of the adventure we also found a Helm of Comprehending Languages anyways).
So maybe less is more. I've played on both ends of the spectrum and while it's a cool moment when you say "hey, I speak X!", it's not one that typically lasts very long or remains memorable.