This is 'Kiss in A Dreamhouse'-era Banshees - the B-side of 'Melt'. Its suitably gothic, but a fairly straight reading of the original carol, which is quite gothic sounding in the first place I guess. Sung in French with, I think, Siouxsie's voice multi-tracked. And its got bells on it.

Other Christmas songs:
Fairy Tale of New York - Christy Moore
Cajun Christmas
Il est Ne le Devine Enfant - Siouxsie and the Banshees
All I really want for Christmas - Ini Kamoze (maybe?)
Christmas Lullaby - Shane MacGowan
White Christmas - The Drifters