He probably spoke Aramaic, Hebrew and Greek, with different levels of fluency. He most likely could also understand Latin. During the verbal confrontation between the Roman governor Pontius Pilate and Jesus Christ, which language did they use?
As far as that conjecture goes, when the Pharisees were calling for Christ's crucifixion and made the point that Pilate would be no friend of Caesar if he didn't give the order, I wonder what language they used, just to diplomatically make the point crystal clear?
Most of his peers would also have been multi-lingual, as Greek was the lingua fraca of the time, as English is today (it might be Chinese or Arabaic in a hundred years...); Hebrew was the religious language and Aramaic was the common language of Jews in Israel.
So much for the ancients not being as "smart" as modern Western man - most of Christ's contemporaries most likely spoke three languages. I wonder how many of us do so on a regular basis?
They also lived under the Roman banner, with Latin the official Roman language. It's a matter of history that the Catholic Church later spread the Latin alphabet as the underlying script of Western European languages, and the Byzantine Church (later the Orthodox Church) the Greek alphabet for most Eastern European languages, including Russian for example which looks like Greek.
When He was speaking to ordinary Jews in Israel, which was almost all of the time, He'd have been speaking Aramaic.
Which is the reason the allegedly different senses of "rock" in His declaration of Peter as the "Rock" is a load of tripe. He'd have been speaking Aramaic at the time, and the word He would have used was Kepha, with no differentiation in either use of the word.
It was only the rules of Greek grammar which caused the change, when the Gospels were years later penned in Greek.
To elaborate on this, using an example from my own life, I did German at school. I've forgotten most of it.
But to use a simple example, "the table" in English becomes "der Tisch" in German, with a masculine gender. Now when I translated the English "table" into the German "tisch", in no way did I feel a masculine sense. As far as I was concerned, the table was still just an "it", of neutral gender in English. But I had to obey the German rules of grammar.
How a native German speaker "feels" when confronted with the masculine gender for a table, I have no idea. I would need a German speaker to tell me. But as an English speaker translating the word "table" into "tisch" I still had my native English (or Australian) sense of the table as purely neutral - it was just a thing.
The same thinking would have applied to the translators who transcribed the oral tradition of Christ's Aramaic speech into written Greek text years later. They'd have had a singular sense of the word "Kepha", and not some variegated Greek sense due to it's grammatical rules.