Many scholars today believe that Aramaic was Jesus’ mother tongue. They also believe he probably spoke some Hebrew and possibly some Greek. I’ve never studied the question in detail but have trusted the scholars that I’ve read. Inevitably when I’m reading a book I find some nuggets buried in the endnotes which far too many readers ignore. I read the following in Gary Anderson’s book Sin: A History (Yale University Press).
“Scholars vary in their opinion as to how fluent Jesus was in the various languages with when he was familiar (Aramaic, Hebrew, and Greek). Most New Testament scholars assume that Aramaic was his mother tongue and that Hebrew was a secondary language. For a good survey of such issues, see Joseph Fitzmyer’s classic essay ‘The Languages of Palestine in the First Century AD,’ which has been reprinted in Stanley E. Porter, ed., The Language of the New Testament Classic Essays (JSNTSS 60; Sheffield, Eng.: Sheffield Academic Press, 1991), 126-62. Although he sides with the view that Aramaic was probably the mother tongue of Jesus, he does concede that there is good evidence for Hebrew as well. Part of the problem is that the best scholarship on the Hebrew of the late Second Temple period is being done at the Hebrew University and is written in modern Hebrew. Only a handful of New Testament scholars could follow this discussion, and I know of none who do. As a result, the case being made for Hebrew as a living language in the first and second centuries CE has gone unnoticed.” (p. 215n.1)