I'm pretty sure the word is not parody, but it's something like that.

I have a good reason for taking a well-known movie and using the shell of it to house my next story. The opening scene and the principal characters will immediately be familiar. But of course, it will veer off; the characters will stand in much the same places, but will have different motivations and personalities. The story will have echoes of the original, but not the same substance.

I'll do my best to make it as interesting and engaging as possible, but it won't necessarily be funny. A parody must be funny, mustn't it?

Underneath the title, I intended to write: A parody based on the 19xx film, the so-and-so, but as I was working out the kinks and twists and turns, I began to see that it was not as comical as I thought at first.

Is there a word for what I'm trying to make? A parody that isn't funny?

Don't say plagiarism, though. It isn't that, either.