Movies where the couple has a J/E quality? Oh wow. This is going to sound really dumb, but Lady and the Tramp definitely has that...proper young female seeking something more meets charming outsider with a heart... I know, you want humans.
Ah! I have one! Notorious. It is an Alfred Hitchcock thriller made in 1946 and it is a masterpiece. Cary Grant and Ingrid Bergman. Summary....okay, stay with me here, but Ingrid Bergman is the daughter of a Nazi. She's a party girl and an alcoholic. Detective Cary Grant makes her an informant and sends her to South America, and through all the danger and intrigue and 1940s banter, they fall in love.