Chanakya was a resident of Taxila in Mahavansh Tika and as per Parishisth Parvan he was resident of Chanaka village in Golla District. Chanakya was a learned man of his time and he would have spoken Sanskrit, Pali, Magadhi (as he spent a major time of his life in Patliputra as it's minister and power behind the throne) and the language spoken in Taxila that time and probably he also knew kharoshti script. The similar languages were known to Chandragupta Maurya as well because since his young age he was studying under Chanakya and spent a lot of time with him.
If Chandragupta Maurya was indeed Sandrocottus, he might have had known a little bit of Greek and Persian as well if not fully fluent.