While Common is the “human” language of most D&D games, here it is called Rumanic and reflects the trade language of the land. The Seven Kingdoms were all once part of a vast empire from which Rumanic is derived, however since the collapse, the long years of relative independence has lead to most lands reverting back to their hereditary languages. What this means for you is that Rumanic (which is Common) is a good language to have and will be understood by a number of people, especially those in bigger towns and cities, along with most traders, but there will be people that only know a specific dialect language. Here are the seven languages primarily used in the Kingdoms: Rumanic, Gahalec, Norfren, Oslovik, Nimuran, Morosian, Lansvig.
The languages mostly commonly used in each kingdom can be found on the specific pages discussing those regions here.