Well,
I was at a talk the other day discussing the similarities between Scandinavian (mostly Norwegian)and Scottish versions of some of the Child ballads.
If you think of the antiquity of some of these songs and the long-standing links between the UK (but Scotland and Ireland in particular) and Scandinavia, then it shouldn't some as much of a surprise, should it?
Furthermore, in one of the Ballads, the Two Sisters (Binnorie) there was reference to links to motifs in versions that have known Balkan themes.
Child himself discourses on known examples of mostly Scandinavian and Southern European versions of the Ballads in his work, as well as versions from Germany and Poland. In fact he implies that the Ballads would have been pretty much common currency, at least in terms of themes if not language...
As for tunes, I'm not so sure, but I would think it reasonable to believe that there will be common or similar tunes emanating from Central Europe and having been carried here by Romany or other itinerant peoples, though I will say I don't know of any. Which may be more of a comment on my ignorance regarding tunes/preference for traditional songs...

Not quite sure if this is relevant as much of the thread so far has concentrated on the Celtic parts of Europe, but there is Northern Europe too, and historically the languages there would have been similarly Germanic in origin...

andymac