I have always wondered this, because at the time they spoke Latin, correct? Would it sound similar? Completely different? Any insight into this would be great; this has always been a blurry topic for me. Thanks!
His name would've been pronounced "Yoo-li-us Kai-sar". There was no J sound in Latin at this stage, Cs were hard, and the "ae" diphthong sounded like the English "eye".
There's a two-year-old comment from this subreddit that goes into detail about the evidence we have for how "Caeser" is pronounced. It's a great post.