The film is Werner Herzog's 1979 Nosferatu, Phantom der Nacht
The music is a Georgian Folksong, spelled variously Tsintskaro/Tsintsqaro/Zinzkaro/Winwyaro, which means "at the spring", and it is performed by the Georgian vocal ensemble Gordela.
The lyrics translate as:
I was passing by the spring.
There I met a beautiful woman with a jug on her shoulder.
I spoke a word to her and she left, offended.
I was passing by the spring.
Wikipedia records that Gonashvili died in 1985, at the height of his fame, as the result of a fall from an apple tree, which somehow fits with the song, and indeed Herzog's scene, with its implications of the fall of man and a loss of innocence!
Here is a link to a poorly copied rendition of the scene on YouTube.
The original Nosferatu is public domain, and you can watch the whole thing on Youtube if you like (but do yourself a favour, and get a DVD).