The Wicker Man is chock-full of folk songs, albeit perverted by the genius of Paul Giovanni and the 'group' Magnet (called Loadstone on some editions of the film) which featured the singing of Sheila Mackie and the fiddling of Ian Cutler (who still inhabits folkish realms in association with Dave Cousins of the Strawbs). TWM is a seminal inspiration on the current crop of 'weirdlore' folkies - indeed you're just as likely to hear Giovanni's tunes to Gently Johnny & Corn Riggs, as you are the traditional ones.   


Better still (in my view) is Pasolini's Canterbury Tales which features a collage of REAL folk songs (note: there is no debate about what Folk Songs are, only academic quibbling over the details) mixed with medieval music, all of which was assembled by Ennio Morricone. The film kicks off with Francis MacPeake's The Owld Piper. For a detailed account of the songs used in the film see:

http://anntheword.blogspot.co.uk/2012/04/folk-songs-from-pasolinis-canterbury.html