I usually think of Old Music as anything roughly before Punk and Metal began.
Francoise Hardy - Si Mi Caballero (1971)
This album was composed in collaboration with the Brazilian guitarist Valeniza Zagni da Silva (Tuca). It's really mellow.
Serge Gainsbourg - Chez les yé yé (1964)
Serge Gainsbourg is kinda like a French Cole Porter. He was a musical genius. This is one of his earlier songs. I found out about it because April March did a cover of it.
Frank Sinatra - How About You? (1956)
This song was originally written for a 1941 film that I've never seen called Babes On Broadway, starring Judy Garland and Mickey Rooney. I really like the song, the lyrics are cute too.
Audrey Hepburn - Moon River (1961)
This is the original version of the song, written for Breakfast At Tiffany's. Audrey Hepburn wasn't a singer (this was the only song she ever recorded), and so the song was written with her limited range in mind. The Frank Sinatra version's great, too, in a different way, but I prefer rhis one.