How does Camus tackle existentialism?

At the end of the story, Daru is left in his little school room defeated, full of existential angst. It doesn’t matter that he let the Arab prisoner make a choice, It doesn't matter that Daru cares more for Arabs than he does for the French. In the end, Daru will always be seen as French because he is white and looks French. No matter what he does or says, things will end the same way.