Meursault's tone as narrator of The Stranger is apathetic and detatched. He doesn't show much of an interest in anything other than physical pleasure, and even then he shows no enthusiasm. Albert Camus has created Meursault to represent an absurd hero according to his theory of Abusurdism. Similar to existentialists, absurdists recognize that there is no true purpose to life and believe the universe to be impervious to the needs and desires of mankind. They believe the world is full of chaos and rather than attempting to fight against it, they succumb to life's struggles and live moment by moment for nothing other than the experience. This is how Meursault approaches his life and causes him to be so emotionally distant from the reader.
Meursault is both a nihilist and fatalist. Some good tone words to use are apathetic and uncaring. Some other good ones are transparent, unbiased, truthful and blatant. Meursault considers himself a rational human being and prides himself in being as objective as possible about the events surrounding him. He doesn't try to hide anything.