The song is called "How Can Love Survive?". Actually, it was never in the film version, only the original stage production. I don't know if it's included in any revivals. Two other songs were also eliminated when they made the movie: "An Ordinary Couple" and "There's No Way To Stop It". You can hear them on the original Broadway cast recording.
Two new songs were added for the movie by Richard Rodgers: "I Have Confidence" and "Something Good". Oscar Hammerstein had died so R. R. also wrote the lyrics.