Greek is the big international language, Gaulish would cover the major number of Barbarians and not sure after that.
Greek would indeed be the "common tongue" - it dominated Greece and the Balkan region of course, but also Egypt under the Ptolemies, and shared equal status with Persian in Seleucid territories. The Greek alphabet was the common writing system across non-Latin Europe, from the Slavs in the east, all the way to the Belgae and Celtiberians in the west (though they spoke their own languages.) Even the Romans considered it a trade language and language of the learned.
Phoenician would probably be the second-most widespread language after greek, being a major trade language. Carthaginian influence spread it around hte Western Mediterranean, south into Africa, plus of course its homeland in the levant (where it remained a spoken language using hte Latin Alphabet until the 7th century or so.) Among the Romans themselves, it would of course be third, after Latin and Greek (you probably didn't want to speak Phoenician after the Punic wars...)
There were several Celtic languages, which can roughly be divided into three relevant continental groups - Gaulish (In France, Italy, and Switzerland), Celtiberian (in Celtic Iberia, of course) and Noric (southern Germania and central-eastern Europe.)
other relatively common languages of the period and area would be Illyrian, Dacian / Thracian, Late Kemetic, and Persian.
"Rare" languages would be Germanic, Slavic, the remaining Celtic languages (galatian, Lepontic, belgian, breton), Etruscan, Paleohispanic languages (Iberian, Basque), Old kemetic, Hebrew, and the Berber languages. These might all be less rare among long-lived races from these regions, elves and such.
Which brings a question - are there "racial languages"? How deep into "fantasy history" are we going here, are there Elvish nations beyond italia? Was Sicily a gnomish holding until its capture by Carthage, then Rome? Are Carthaginians Dwarves?