Great question! To be honest my very first caution to you is:
Don’t try to make it sound too old. Not in the sense that you’re in the wrong era, but in the sense that, as a reader, I really don’t want to go through a whole book where people use ‘thee’ and ‘thou’ in every sentence. The point is, if you try too hard to make your fantasy writing sound old timey, you might end up strangling the writing. It’s okay to have characters use more modern ways of speaking for the reader’s sake. It’s also okay if your story sounds a little modern–as long as the setting and characters are well established, your reader most likely won’t fault you for it. It makes reading it easier.
Given that, under the cut are a few tips that I can think of to make your language more fantasy-like.