There is an issue in how you phrase the question. "Jesus" is a transliteration of "Yeshua", a relatively common first name at the time. But "Christ" is the Greek translation of "Messiah" which means the "anointed", and is a mythological savior figure which was foretold by the prophets. The Christians believe Jesus was this messiah, while mainstream Judaism did not. Using the term "Jesus Christ" is basically a declaration of faith that the person Jesus was indeed the Messiah, so this is problematic for a historian.

But the question if the person Yeshua aka Jesus, which some people believe to be the Messiah, did exist as a historical person - this is a question which can be answered as a historian. And the answer given by most historians is that he most likely did exist, and the evidence is the four gospels in the new testament. While these four narratives are embellished and contains parts which are clearly legends, they are most likely originate from real events and real persons.

This is a question that's been asked fairly frequently in this subreddit, so there are earlier answers. In this answer, /u/talondearg summarises the evidence (from both Christian and non-Christian sources) for the existence of Jesus. Their conclusion is that Jesus was, most likely, a historical figure. They also made a slightly longer post, coming to the same conclusion here. Another user, /u/jasoncaspian, gives more context to the argument here. He too concludes that Jesus was a historical figure.