It's Irving Berlin's "Blue Skies":
(Don't be misled by the image: the song isn't on that album.)
Wikipedia lists only two recordings of "Blue Skies" by Sinatra, both from the 40s, and sure enough I can't find anything later. I'm guessing this is the 1946 version. I wonder why Frank never revisited this classic? How I wish we had a few more takes on it, perhaps a heartfelt treatment a la Bing that implies some clouds on the horizon, or maybe a gently swinging Riddle arrangement in the style of Songs for Swingin' Lovers.
It's got to be one of the greatest songs of all time and more singers have recorded it than you can shake a stick at. Here's one I'm especially fond of:
Chuck Brown could sing.