Hey, this is a good topic. I haven't thought of this in psychological terms.
Now, I'm not a psychologist, but Franklin does strike me as a sociopath. I mean, he calls his ex from a strip club, asking her to get back together (or something like that). Clearly he has no idea how human emotions work.
Trevor on the other hand is full of emotions, except they are completely off the whack and confused. That might indicate some sort of a neurological problem. I don't know which, but he might be schizophrenic combined with psychosis or some severe mood disorder.
Michael I don't know, he seems to be a fairly normal guy stuck in bad situations. I'd guess he is suffering from guilt and overcompensating. I don't think narcissists tend to go to psychiatrists and talk like that. In fact, narcissists feel great about themselves, unlike Michael who is a miserable wreck. That's quite the opposite of narcissism I think. If anything, I'd say he's an adrenaline junkie, not much more else.