There's actually a few songs Emma can sing if you go back to the Karaoke parlour, but if you mean on the very first date there then the song is called "Shambhala (Just Imagine)" by the amazing "Snowflake" and you can find the original right here:
http://dig.ccmixter.org/files/snowflake/57859
Also, all songs are credited in the "CREDIT" file in your game folder, as well as in-game :)