A ramble through the Oxford Book of Carols would point out a number that probably had more pagan lyrics and then were "cleaned up" for church use:
"Tomorrow will Be My Dancing Day", "Furry Day Carol", "Holly and the Ivy" (of all the trees that are in the wood/ The holly bears the crown), "Holly Bears a Berry", I know there are more... possibly even "Lulley Lulay".
Blessings,
Barbara