I have a book full with British folksongs that have been translated into German. Most of them I never have heard sung in German.

Tunes to which I have heard German lyrics actually sung:

A man's a man for a' that
Should ould acquaintance
Greensleeves
A round (I don't remember the title) "Hey, ho..."

Several shanties have German lyrics too.

When I sung a German song at the Eurogathering most of the English speakers did know Englsih lyrics to that tune.

Sometimes, know tunes (from Britain or Ireland) are used to put music to German lyrics with no known tune:

Follow me up to Carlow has been used this way.

I'm sure a large book can be filled with 'European' tunes.

Wolfgang