Dang. Just looked it up. It's a song about a girl he met once and was dating someone else, but he still wrote a damn ballad and sent her a copy. Then she had to live her life surrounded by a song about a stranger's feelings for her.
And looking at the lyrics, they're sweet if said about a long-distance partner, but really weird to sing to a vague acquaintence.
Watch the damn scene. She is trying to brush him off. She wants to leave, and he is not letting her. She is politely saying no, and he is politely forcing her to stay. Even if it is due to social pressure, let her fucking leave.
"Well maybe just a half a drink more" is said when he has just snatched the coat off her back and is still holding it. Her face is a picture of resignation, not coy flirtation. She then asks "say, what's in this drink" and puts it down with a scowl on her face.
This is flirtatious by the standards of a Sean Connery movie.