If you're hunting for something that nails the texture of medieval life more than the sword-swinging, you can't beat Maurice Druon's 'The Accursed Kings' series. It's political, brutal, and reads like a primary source sometimes. The way he details the financial strain on a kingdom, the logistics of a siege, or the messy dynastic squabbles—it's all rooted in deep research. I had to pause a lot just to look up some historical figure and was blown away by how closely he adhered to the record.
That being said, sometimes the very thing that makes it 'accurate' also makes it a dense read for some. It's not a light, escapist fantasy romp. For a slightly more narrative-driven but still impressively researched take, I'd put in a word for Connie Willis's 'Doomsday Book'. It's time-travel sci-fi, but the 14th-century Oxfordshire setting is rendered with such painful, meticulous detail about disease, social hierarchy, and daily survival that it feels more real than most straight historical fiction. The accuracy there is in the emotional and sensory experience, not just the dates and battles.
Ultimately, 'best' depends on whether you want the macro-politics of kings or the micro-reality of a village during the plague.