I'd think comical ones would work better, which seems to rule out most of the AAA stuff you see on the PS4 and Xbox1. Really, it seems like nintendo would be the best bet, but there's no franchise I can think of that would work well as a cartoon... Cartoons, and I say this as a person who loved what we had in the 80's, 90's, and early 2000's, are of a quality today that don't leave as much room for half assed product placement.
Sonic seems to be getting by, though... I suppose Zelda, if done right, could work. Splatoon would have to be rather different from the game given paintball matches wouldn't really fill a series.
Maybe that Yo-Kai watch or w.e it is could be akin to pokemon? Is that already a thing?
Umm I know Ubisoft is trying to push Assassins Creed into the mainstream through movies and merchandise, but that doesn't seem like a kids cartoon at all given the murder, religion/historical figure bashing etc.
Really, with blizzards sense of humor I think they could make a warcraft cartoon work, but that'd never happen.
Video games should probably just remain video games... Some seem to work like Sonic, but most don't :p