You could use Colonialism as a critical theory. The novel takes place in Algeria presumably in the early 1940’s since the book was published in 1942. France occupied Algeria from 1830 until 1962.
The subject of colonialism and race is often obscured by the philosophically overwhelming themes of Absurdity and Existentialism. But the aspects of race and colonialism play a central role in the novel. In fact, the relation between French-Algerians and Arabs in the novel reveals a Eurocentric perspective. Meursault only associates with other French-Algerians. The Arab he kills is never given a name. The Arab is literally some “Other” person who unfortunately falls into the path of Camus’ Absurd hero; and here, “Absurd” has to refer to the philosophy of Absurdity as well as the general concept of absurd as being irrational and illogical.
Criticism of this novel tends to focus so much on the philosophical aspect that it ignores the racial aspects. Meursault might have arrived at some philosophical epiphany about existence. But his self-involved philosophical brooding should not be an excuse for murder. Meursault is heroic in his absolute refusal to accept the beliefs of society, but he’s guilty of murder. He does what he can to mentally remove himself from this society (and/or the world) but he still exists in it and must acknowledge that his actions will engage others. He never really acknowledges this.
The fact that the Arab is never given a name is really telling. I don’t know if Camus was making a subtle point about colonialism with this move, but it is there whether he intended it or not. This is a clear example where a white European’s racial “Other” plays victim to the member of the colonizing nation. Meursault is arrested and executed but this doesn't erase the fact that a man was killed. The novel is completely focused on Meursault's quest for meaning. The Arab simply becomes a statistic: the "one" that has been killed.
You could argue that Meursault's indifference is not racially motivated; he would have killed anyone of any race that day. After all, his nonchalant attitude was the same with his mother. But you could also argue that colonialism and race did play a role. Reacting to his mother's death and actually killing another person are two very different things. Meursault is the narrator, so it is he who does not give "the Arab" a name.
The court and certainly the priest seem to be more appalled at Meursault's belief system than they are with the murder. They are more concerned that his religious and cultural beliefs are different from theirs. Thus, they are more unsettled that he is unlike them: an "Other." It is his difference, not his crime, that they focus on.