Only those with high education were able to speak Greek
Jesus and multiple disciples almost certainly spoke Koine Greek in addition to Aramaic. Andrew and Philip are even Greek names.
His adoptive father was a tradesman, and Greek was being used as a lingua franca for business in the eastern Mediterranean during the 1st century. There is archeological evidence to support Greek usage in Sepphoris at that time, which was 4 miles from Nazareth. In John 7:35 the crowd even speculates that Jesus might leave them and go and teach Greeks, which presumably means they thought he could speak Greek. Some scholars believe the Sermon on the Mount could have even been delivered in Greek, considering the large diaspora of Jews present.