It seems to me that in Eorzea they have a unified language because everything from road signs in Thanalan and La Noscea to the Ironheart Map use the Eorzean alphabet. However, the beast tribes and other creatures (e.g. goblins, Mamool Jaa) do have their own language and their broken form of Eorzean Common often contains artifacts of their native tongue as explained by Fernehalwes. For example, the goblins often jumble two or more words in Eorzean to create a new one that would have had a clearer meaning in their own language like busytalk, longstop or unguest; the slyphs also appear to use "these ones," "walking ones" or "those ones" as general pronouns instead of he or she.
I would be interested to know more about how the modern Eorzean language came to be and how the alphabet was standardized. Did the Nymeans, Amdapori and Allagans have this common language? Or is it much more recent?