The remake.... its been done. Sorta.
http://www.imdb.com/title/tt0419198/
I didn't realize it until the final scene, but the 2005 Roberto Beninini film "La Tigre e la neve" (The Tiger and the Snow) is a thinly veiled remake of City Lights.
Maybe it's not fair to say its a remake. I mean, that would be like saying A Bug's Life is a remake of Kurosawa's "Shichinin no samurai"(The Seven Samurai). At their cores they are the same story, but with wholly different characters and adventures.
I guess the fact that I didn't even recognize the similarities til the end (at which point in retrospect it all becomes very obvious) is a good sign. Unfortunately the ending doesnt hit home the way it does in City Lights.