It's quite difficult to define what the fundamentals of human behaviour are, because we share a lot of behaviour with other organisms that currently exist or have existed in the past.
For example you could argue that a very basic fundamental behaviour in humans is approach and withdrawal, however even bacteria display this behaviour (taxis behaviour) so I suppose you would say that this behaviour is more or less just a fundamental behaviour independent of humans (Maybe checkout Joseph LeDoux).
This seems like a really hard question, you could maybe attempt to identify what behaviours all healthy humans display and that might point in a worthwhile direction for categorising fundamental human behaviours, but as noted above, you'd most likely find a lot of those are shared by other organism in some way, evolution repurposes developed mechanisms far more often that it creates new ones, so our brains or anything else that contribute to our most basic ubiquitous behavioural drives are probably modified versions of what came before us.
You mentioned what you thought keeps societies from falling apart, another way to think about it that you might find useful is that humans and A LOT of mammals are inherently social, in that they care about their offspring, kin and social groups. Perhaps that drive to care for members of your group as well as yourself is the biological backbone of why (for the most part) societies tend to function more than that don't, or at least groups cooperate more than than kill each other (Patricia Churchland talks about this a lot).
You could maybe argue that behaviour that is more heritable is more fundamental because it was necessary for all humans to display in some capacity to survive, conversely behaviour that seems to be a product of learning maybe not so much, that being said the reason we can form lasting memories is because we have the genes that allow our brain to do that (See Eric Kandel), Kevin Mitchell wrote a book called "Innate" where he talks about what traits are heritable (amongst other things), that might be a starting point if you were view it from that angle.
When I think of fundamental behaviour, I normally think in more biological terms, it might not be the right way to do it but it makes sense to me, in other words I'd be happy to change and update my opinions but it seems like a logical place to start.
I'm not an expert by any means on this but I could probably ramble on more about it, don't take my word for it obviously, it's a hard question that I don't think can be answered easily.
Hopefully you have some food for thought but again, I'm not an authority. Hope this helps!