You're testing my memory here. It's twenty years since I read it. From memory I think the title translation of the "The Outsider" fitted better than "The Stranger" in some ways (though lost the double-meaning). The idea was that he had become detached and didn't feel the same way as other people (and shocked them by the way he didn't go through the usual emotions at his mother's(?) death) etc.
From the little I remember it went beyond the normal tenets of Stoicism (in The Kipling-esque sense of equanimity in the face of being buffeted by external events) and headed off into the realms of someone becoming detached from humanity altogether. Not sure now or then whether that was intended as a credo, a warning or a statement of existential bleakness.
(Random weird fact. The Cure got in trouble for writing a song