I am looking for an old romantic film that has great sentimental value to my family, and would be grateful if you could help me find it.

Movie details:
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Was viewed on TV in May-June 1981, so if ever was theatrical likely to have been released before 1981. Likely: much before as it was probably B&W. At least, part of it is.

Movie description:
The protagonist goes back in time to an earlier century, meets a woman there who we remember has something to do with Pianos, Piano playing, or singing. They fall in love.

Turns out the woman has some malfunction of the heart: deadly in her century, easily solvable in the century the protagonist came from.

So, he goes back to his century (alone) and looks for her there… identifies her as a flight attendant and convinces her to come with him to a hospital right away. She of course didn’t even know of her heart malfunction, which is then easily cured. He then reappears baring flowers to re-introduce himself…