In D&D lore, Common is the language of Humans, but it also tends to be the language commonly spoken throughout the area/world, a lingua franca used so that everyone can understand each other even if they speak different languages. Therefore, it would change and evolve as time passes and its users come from different language backgrounds and have different needs.
My personal belief is that in that sense, yes, Avalir would have had a Common, although it might be unintelligible to a Common speaker in the Dwendalian Empire. We don't have anything official beyond what's on page 9 of the Explorer's Guide to Wildemount (that I'm aware of), but my guess would be the Empire adopted Common over Zemnian as they grew and the Empire subsumed more and more local dialects, since it would be a language almost everyone at least had some passing familiarity with, especially if they were involved in trade.
It's kind of like Latin in the ancient world, or English today.
