Sorry in advance for the length of this reply, but I also enjoy medieval-set historical fiction, though as someone who got my B.A. & M.A. in medieval studies, I have a hard time finding ones that don't make me cringe with inaccuracies :-)
* The Sunne in Splendor/Sharon Kay Penman (Richard III of England)
* Here Be Dragons/Sharon Kay Penman, followed by Falls the Shadow & The Reckoning (12th & 13th century England & Wales)
I have not enjoyed subsequent books by SKP nearly as much, but for what it's worth she has a series on Eleanor of Aquitaine & Henry II, a series of medieval mysteries, and a couple of other books also set in medieval England/France/Wales.
* A Vision of Light/Judith Merkle Riley, followed by In Pursuit of the Green Lion & The Water Devil (14th century woman dictating her life story to a disapproving monk)
* The Daughter of Time/Josephine Tey (might not be ideal for you, as it's about a modern-day detective looking into Richard III & the princes in the tower, but it's phenomenal)
* Queen of Swords/Judith Tarr (Melisande, the heir to the kingdom of Jerusalem during the 12th century-- Crusades, in other words)
Judith Tarr has also written other books set during the Crusades, but they have more of a fantasy bent, which may or may not appeal to you. If that sounds interesting, start with The Hound and the Falcon, an omnibus edition of the trilogy (the other books are prequels/side stories)
* The Good Men/Charmain Craig (Cathars and the Albigensian Crusade in southern France)
* The Treasure of Montsegur/Sophy Burnham (ditto)
* Jerusalem/Cecelia Holland (story of Templar knight during the 2nd Crusade)
* The Firedrake/Cecelia Holland (Norman conquest of England)
I only recently started reading Cecelia Holland, but so far she's fantastic. She has quite a few freestanding historical novels, many of which have medieval settings, as well as a recent series set during the Viking era.
* Morality Play/Barry Unsworth (14th century England)
* The Ruby in Her Navel/ditto (12th century Norman Sicily)
* Katherine/Anya Seton (late 14th century England; tells story of mistress of one of the sons of Edward III)
If you like historical fantasy at all, I'd also recommend Guy Gavriel Kay. Many of his books are set in fictionalized versions of medieval Europe. Unlike a lot of historical fantasy, his books are very well researched-- he seems to fictionalize the settings more so he can tweak details/time frames to suit his plot, instead of just out of laziness with the actual historical facts, if that makes any sense. At any rate, here are the books of his I'd recommend:
* The Lions of Al-Rassan (El Cid & the Reconquista in Spain)
* A Song for Arbonne (Cathars & Albigensian Crusade in S. France)
* The Last Light of the Sun (Vikings in "Dark Ages" England)
* Sailing to Sarantium/Lord of Emperors (5th c. Byzantium)
Okay, must stop now before I want to reread my *entire* bookshelf. Enjoy!