Here’s what Fredriksen says about the use of Latin at the time (I pulled it from Nexis):

And while Aramaic was indeed the daily language of ancient Jews in Galilee and Judea, Latin would scarcely have figured at all. When the Jewish high priest and the Roman prefect spoke to each other, they would have used Greek, which was the English of antiquity. And Pilate’s troops, employees of Rome, were not “Romans.” They were Greek-speaking local gentiles on the imperial payroll. Gibson’s pious evocations of historicity rang more than a little hollow. How much homework had he actually done?