I think the trick is to write something that is modern enough that it flows with your audience, but not so modern that it screams, well, "Modern!"
If you use medieval jargon, it's like a old man trying to read 1337 speak (or me trying to write 1337). It's almost an entirely different language, and even if you know how to use it properly, your audience won't understand it. If you use terms like "thee" and "thou," you end up sounding pretentious and distracting. In fiction (with the possible exception of literary fiction), don't use prose that distracts your audience from the story.
But what is just as distracting as theeing and thouing is using phrases that are, blatantly, modern. If a character says "It's sick!", they better be saying it's ill, not saying that it's good. And if they say "It's cool!" they better be referring to the low temperature, not the fact that it's popular.
Good luck with your story. The essence is to convey what you want to convey without annoying your audience.