I think he was ESFP 8w7>7w6>3w4 Sx/Sp
I know he's usually typed as an ENTJ or ESTP, but neither work in my opinion. he's clearly Fi/Te, so ESTP is out and I have a lot of trouble seeing him as detached enough to be a Te dom. ENTJs strike me as much more controlled and planned out and, while I don't tend to like to use Keirsey archetypes, there is absolutely nothing NT-ish about Frank Sinatra.
granted, there is a fair amount of Te in his music, but it serves his Fi, not the other way. given this and the clear Fi and Se, I think ESFP is the best fit