I just sad here reading up on some of his writing. And also of Jung who said that he thought Freud was extroverted, but so very neurotic that he was hard to type.
Now in many respects I think the "obvious typing" of him is INTJ. His theory of the psyche, and the defense mechanisms are all very remnicient of NTJs. Then there is the unacknowledged cribbin' from Nietzsche (which has recently been documented; he knowingly covered his tracks). And then there is the strong will with which he browbeat the psychoanalytic community into always giving him his way. Also he had many compulsive traits, again suggesting NTJ. But alas, also, he was the eldest of six (i think) siblings and was the only one to get his own room because the parents had such high hopes for him - pretty much the textbook way to traumatize a child into becomming compulsive.
Yet on the other hand there is also the fetish-ation of Ancient Greece; Plato as a model of the Superego-Ego-Id, and Sophocles / Oedipus. He looks for precedents or allegories akin to his own theories to a degree that would suggest almost semiotic interest, a field that is indeed mostly bullshit and has never attracted many NTJs. (This is seen again in his book on Leonardo.) This overreliance on past precedents and the elevation of Ancient Greece suggests repressed Si; I see it in myself. Also, in the Cambridge Companion to Freud there is an essay about his private feelings when he (a) recieved a coin with himself on one side and the Greek sphinx on the other (okay, that could suggest some Fi-ness) but more revealing (b) his mythologization of Rome (the city); wanting to go there for many years; having fantasies about it in his head, hoping that it would be a transformative experience to visit that city. Again I identify with this sillyness, and I think it suggest Ne, Si and some Fe.
Looking at Freud's work, one sees almost only Ni / Te / Fi. But still there is something there, which one would not expect from NTJs-writers: There is the constant, hestitant, attention to the reader and to what the reader might be thinking; such allusions are scattered throughout most of his texts and are often referred to in Freud scholarship. In general they are quite odd for a scientific/academic writer. For out purposes, its more Foucault-like, ENTP-like.
So the point is that Freud seems to combine the traits of both an INTJ and an ENTP. And while the INTJ typing can sensibly stand on its own, albeit with a few anomalites here and there, nobody would ever understand / accept the ENTP typing.