Monsieur Meursault's tone is generally dispassionate, unemotional, impassive, unperturbed and self-possessed.

Examples that support these adjectives include the novel's opening lines:

Mother died today. Or maybe yesterday; I can't be sure.

The death of a parent is usually a watershed moment in a person's life, but Meursault is virtually unmoved by her death and only feels slightly self-conscious when he realizes that people are judging him for his lack of emotion.

Even when Meursault kills the Arab on the beach, his first thought is:

I had shattered the harmony of the day

which would, by most people's estimation, be a hugely understated reaction to taking another person's life.

Even when he faces his own impending execution, Meursault's tone is rather expressionless. He says,

I opened myself to the gentle indifference of the world.

In a very telling confession that immediately follows this line, Meursault finds the indifferent world much like himself.

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.