This still-shot comes from the inspired, short, legendary TV series:
https://en.wikipedia.org/wiki/The_Addams_Family_(1964_TV_series)
Now, if I tried to talk about The Addams Family here, then we'd be here all day, and much of that time would frankly be down to me bumbling around for words and specific episodes I half-remembered.
But actually, the whole franchise started with Charles Addams' deliciously, lovingly-morbid Addams Family comic art & strip series. You're in LUCK though if you were looking for that kind of thing, because one of our comics-sharing historians here has you covered!
That would be my mate @nocturne@slrpnk.net, who's taking the time to scan and upload his books / material to help create a comprehensive, major picture of the classic Addams cartoons.
That goodness is shared at this sub (altho there are maybe other places I don't know about):
!comics@lemmy.blahaj.zone
Specifically calling him Bubele, which first happens in episode 2, season 1, Morticia and the Psychiatrist. Initially Gomez's response to the pet name is mild, but becomes more exaggerated as the "Tish, that's French" shtick evolves.