This 1963 pop song plays just before Rory and Dean kiss and make up, and follows Lorelai as she goes to see Luke in the diner. One Fine Day was written by Gerry Goffin and Carole King, and recorded by the girl group The Chiffons. It was a hit around the world, going to #5 in the US.
The song seems to be a comment on Lorelai’s feelings for Luke – that “one fine day” he will want her for his girl.
The Annotated Gilmore Girls 