This is an interesting question, as there has been a debate amongst theologians and historians about the nature of Jewish society in Judea during period which Jesus allegedly lived, as while many Jews lived under the influence of the Greek and Roman worlds, there was a strong movement amongst the Pharisees and other Jewish leaders to move back towards a purer form of Judaism that followed the Torah and used Hebrew as the language of religion.
After Alexander conquered the Levant, and subsequently died in 323 BCE, Egypt and the Levant were ruled by the Ptolomaic dynasty, with Judea then ruled by the Seleucids, and finally after a Jewish revolt in 165 BCE by the Jewish Hasmonean dynasty. Eventually in 63 BCE a civil war broke out in Judea between rival Jewish factions, with the end result being that the Herodian dynasty came to power through the use of Roman support, which turned Judea into a Roman client state.
Now, this is important to note for several reasons. The first is that the Romans were able to bring commercial stability to the region, which in turn enabled an educated merchant class to develop who were fluent in Greek, Aramaic, and possibly Latin. Aramaic was the common language of the people (a language that is still spoken as Caldean today), and where traders gathered Greek was the still the predominant language of commerce across much of the old Greek influenced areas.
Second, David Suchet's documentary series did an interesting breakdown into the life of the apostle Peter, in particular looking at the culture of the Galilee region of northern Judea where some of the apostles including Peter were drawn from. Galilee is close to trading hubs of the Levantine coast, and as such fishermen such as Peter would have been immersed in the Greek language of trade, as well as the Aramaic culture of Judea. So, while it is an educated supposition, it is likely that merchants, traders, and those who interacted with them would have been able to speak Greek in order to facilitate commerce and trade across the region.
Sources:
The Orthodox Church by Catherine Clark
HELLENISM (from έλληνίζειν , "to speak Greek," or "to make Greek") by Carl Siegfried, Richard Gottheil
Documentary series - In the Footsteps of St Peter - David Suchet
Here's a post with an answer by u/Goddamnpassword as well as others that talked about this to tide you over until you can get a proper response. It's possible, but unlikely that he spoke Greek or Latin. Being well educated for Jesus' time and place mostly meant being fluent and literate in Hebrew, as evidenced by his ability to discuss and debate scripture with rabbis and Pharisees.