Most people think that it’s likely they spoke a dialect of
Aramaic, specifically,
Western Aramaic.
As for the exact dialect (Galilean Aramaic) that they spoke, it’s extinct.
The closest surviving relatives of Jesus’ Aramaic are now spoken only in a few villages in western Syria; most dialects of Aramaic spoken or used today (such as Syriac or Chaldean or Assyrian) belong to the other branch of the family, Eastern Aramaic.
Since Galilean Aramaic is extinct, you basically have to reconstruct what it sounded like.
Here’s one idea. (BTW, the ‘Aramaic’ you hear in
The Passion of the Christ is essentially a ‘reconstructed’ mish-mash of Aramaic from different periods.)
P.S. It ‘sounds’ (but only very vaguely) like Arabic, because Hebrew, Aramaic, and Arabic are all
Semitic languages.