Pirates have been a favorite subject of films for decades but they tend to take a more fantastical approach with some very well-worn tropes and mythological ideas. I'm curious if there are any films out there that depict pirates, privateers, or what we call the Golden Age of Piracy with more attention to fact than to 1930's tropes about peg legs and parrots.
I've seen "Master and Commander" which is in the same vein although focused on the military side of sailing rather than a pirate/privateer story.
I'm sorry to say, but Hollywood has not produced any film or show that could be called accurate. Everything Hollywood produces ends up playing up to audience demand and not history. It wasn't until a couple years ago that we got our first piece of mainstream pirate media that was above PG-13 (referring to Black Sails), which is interesting considering what a number of these pirates did during their careers. While Hollywood makes tiny steps here and there towards accuracy, it's apparent that most of those steps are implemented into products because of other reasons besides wanting to create an accurate portrayal of pirate history.