I saw the latest version of Titanic, and don't remember the movie that I'm looking for to be similar to that story line. It may be "The Lady Eve" though. Although I think there was more singing in the movie I'm looking for than "The Lady Eve" may have.
I remember the movie that I'm looking for had love "tension" between the two main characters. The man had dark hair (I think he looked like Carey Grant) and I think the woman had light hair. The woman was falling in love with the man, but for some reason the man did not want to have any kind of committed relationship. He seemed like a "womanizer". Maybe this helps???