The First Time I ever Saw Your Face, Ewan MacColl
Will You Go Lassie Go
Cavan Girl, the Dubliners
Red is the Rose (except for the last part)
I Love a Lassie

I thought I knew a lot that might work but as it turns out a lot of romance related folk songs are really sad or they're weird in some sort of way for valentines.

Anyhow if it works for you, here are the rest I know of:

Fear a Bhata
Loch Lomond
The Bonnie Lass o Fyvie
Maids When You're Young, Never Wed an Old Man
Eriskay Love Lilt
Maire Mhor
Teir Abhaile Riu
Åsmund Frægdegjevar, a Norwegian folk song
Danny Boy
The Rose of Allendale
Mo Li Hua (Jasmine Flower), which I hear a lot at home and is sung in Mandarin. It works within context I guess. Not historically, but if you look at the lyrics it could easily be a romance.