There is an idea of a Patrick Bateman; some kind of abstraction. But there is no real me: only an entity, something illusory. And though I can hide my cold gaze, and you can shake my hand and feel flesh gripping yours and maybe you can even sense our lifestyles are probably comparable... I simply am not there. (Je ne suis pas simplement là)
That sentence is a weird one, so I'll give some clues as to when we would use it. It basically means that you are there, and that explanations are not relevant in regard to how you got there, like if a superhero arrives at a totally unexpected moment. Example:
-Toi, ici, chéri? Mais... c'est impossible? -Et pourtant c'est vrai! Ne pose pas de questions. Je suis simplement... là. = -You, honey, here? But... that's impossible! -But it's true! Don't ask questions. I am just... here.
I think of it as "I just happen to be here", not in any official capacity or purpose, but simply "I'm just here".
Of course, there's also also the existential perspective of "be here now" or being in the present moment, rather than dwelling in some other place or time.
Orally, French people mostly say "là", whether for "here" or "there". "Je suis là pour toi." "T'inquiète pas, je suis là."
I started a discussion about this, and some helpful French Duolingoers filled me in: