This recording is currently titled "Love Theme From the Godfather", along with most of the track titles in the releases where it appears. However, the corresponding work has "the" capitalized.
I think lowercase "the" looks very odd here, since it is the love theme from "The Godfather" (the movie), not the Godfather (the character). However, given that there are no quotation marks around "The Godfather" in the track title, the style guidelines seem to demand a lowercase "the".
Maybe we can wiggle out of this by saying that "the" is is not being used as an article here, rather "The Godfather" is a name?