At my wedding Mary and I sang to each other. We sang "Little Turtle Dove" which is a lovely folk song.
"Oh don't you see yon little turtle dove Flying from vine to vine Mournin' for it's own true love As I will mourn for mine.
As I will mourn for my own true love Believe me when I say You are the darling of my heart Until my dying day."
Judy Collin's "Since You've Asked" is a lovely song already suggested.
We had bagpipers pipe in Mairi's Wedding and it synchronizes with the traditional "Here Comes The Bride" for the processional.
It's not a folk song per se but the beautiful "hapa haole" Hawaiian Wedding Song has a lovely melody and great chords.
"Oh How We Danced on the Night We Were Wed"...the "Anniversary Song" has a traditional Russian Jewish melody.
Mazeltov,
Frank Hamilton