I wouldnt chartacterize Rocco and Neri as "society people," but I get the point. Frankie was ....as Kate might put it... a common Mafia Hood... a guy from the streets.

I do think his character changed in the film...keep in mind that he was misled to think Michael puit a hit on him, meaning he spend a lot of time thinking he'd been betrayed. He then broke Omerta for a deal he came to regret and on which he renegged, and in effect he died a broken man. So in all the happy go lucky Frankie who was up on the bandstand looking for an Italian musician became a somber, reflective student of history who "saved" his family and its honor by slashing his wrists.

TB you are correct to note what a great character he is. Frank is truly a tragic character in the classic sense.