I have a very monarchy-esque secret society in my story, and I'm trying to get a better sense of how it would be designed and how the social hierarchy and division of power and duties generally worked. Does anyone know any good documentaries I should give a watch?
Why are you restricting yourself to documentaries? If you want to find something in addition to books, I'd look for academic lectures on this topic, if any can be found on YouTube.
You might check out https://www.futurelearn.com/subjects/history-courses/medieval-history for some free online courses. I've been pleased with the courses I've taken from Future Learn, and they change regularly.
What, specifically, are you looking to learn about? European monarchies varied, from one where the power lay more in the hands of the barons, like England, or ones that were more like absolute monarchies, like France. Or even pseudo-monarchies, like the Roman Catholic Church.
They weren't THAT much of a secret society. They were extremely high profile and visible throughout Europe, with castles, monasteries and other property, as well as considerable wealth (that eventually led to their downfall). They may have had some secretive practises and rituals, but they weren't exactly hiding the fact of their existence.
I am rather ignorant on the subject of history, but I don't remember encountering much talk if at all about secret societies that somehow were close to rulership lines in medieval times. I think that there were people within the rulership forming secret alliances instead. But again, I might be completely wrong. Do you want your story to be accurate or just looking for inspiration that leads you away from writing exhausted tropes?