That's a term originally coined by Cary Grant, if one recalls correctly, describing a young lady who was excessively prim and proper, moralistic and sexually repressed to the point of being rather cartoonish.
One doesn't really recall which Cary Grant movie it was or what actress was in the role of "Miss Goody Two-shoes" - Possibly Deborah Kerr... However, the character Mary Poppins, who admittedly never appeared in any movie opposite any character played by Cary Grant, does come to mind...
I think you are thinking of Father Goose. Good, funny movie taking place during WW2. Cary Grant is an American history professor escaping the real world. He gets recruited by the British Navy (Trevor Howard) to be a watcher. He ends up rescuing Miss Goody Two-shoes and embassy kids. In the end he, his new wife and the embassy kids get rescued by an American sub.