I guess originally they were going to call the film "Baby's in Black" after the Beatles tune but it was too expensive so they switched to "Moonlight Mile." I thought I was familiar with most of the Stones' songs, but had never heard of this one. I don't know if it's a great fit or good description for the film, but it's a pretty song. (So is "Waiting for a Friend" by the Stones.)
There were two things I liked about this movie. One is the idea that the plot and all characters revolved around Jack as Joe and he carried the movie. That is something when he's playing with Oscar-winner heavyweights like Susan Sarandon and Dustin Hoffman. Two he and Ellen Pampano make a cute couple!
more than you wanted to know about "Moonlight Mile" from allmusic:
It seems as "Moonlight Mile" may be one of the rare songs that does not include the presence of Keith Richards. The initial guitar part was written by him and put down on tape but left incomplete until an uncredited Mick Taylor developed it into a full song.
Making up the dominant theme of the song is a beautiful acoustic guitar riff -- played by Mick Jagger -- that has a vaguely Asian feel.
The variation on the riff gets picked up by the lush Paul Buckmaster string ensemble, building the song into a dramatic climax before drifting away quietly, featuring the lovely piano of Jim Price and concluding with a regal string flourish.
"Moonlight Mile" marked a change of direction for the Stones, stretching out from the blues, country, and R&B-based roots music they had returned to after flirting -- with mixed results -- in the late '60s with psychedelia. The Stones had been producing layered but streamlined electric guitar-based records.
In relation, "Moonlight Mile" was an epic production, not only with the sweeping strings, but other studio techniques like doubling Jagger's lead vocal -- a technique he rarely employed.