Because this text is often considered both absurd and existential, the mood and tone are important considerations. First, in part 1, we see Meursault as almost completely indifferent. He is unmoved by his mother's death; he is unmoved by Marie's need for love; he is unmoved by Raymond's and Salamano's cruelty; quite simply, he is unmoved by the goings on around him. As a result, the mood is one of apathy or indifference.
Tone is also very much lacking in the beginning of the text and much of the way through part 2. If tone is ever changed, it would have to be at the end when Meursault begins to understand the error in his ways. Then, the tone is a bit more harsh and the mood is one of frustration.
Mood and Tone in the book are also highly affected by one's initial translation of the title 'L'etranger' - which is often translated as one of two things: 'The Outsider' or 'The Stranger'. For example, one might argue that the title of 'The Outsider' indicates a much more detached character for Meursault, one that is almost ostracised. Whereas 'The Stranger' seems to conjure images, more specifically, of his behaviour. Rather than of his overall place within society.
In response to 'kirstens' answer, you might also wish to question/disagree as to whether Meursault ever does feel remorse for his actions. Does he see his death as simply another effect in a chain of causation, or does it truly move him to sorrow? His denial to turn to religion is contextually interesting and reflects a society, which at the time, was looking to become increasingly secular. We also see this theme highlighted during the opening of the book, during the funeral, when all he can concentrate upon is the image of the sun bearing down upon him. However, it is up to you how you might interpret this image.