The book was published in 1942 and, by all indicators, was meant to be contemporary. There is no mention of the war, however. So, let's date it to the late 30's. I am not sure if the Vichy Government treated Algerians differently.
Edit: I only mentioned The Stranger because it made me wonder about the Legal system's position on white-on-arab crimes at the time. I realize that, in the context of the book, he is more so on trial for not following societal norms.
However, I a quick google search confirms that Algeria was absorbed into France as a Department. Were there special laws that governed Algeria? Did they make special mention of race? Did they explicitly elevate white people, degrade all others, or both?
Wasn't one of the major themes of the novel was that he was getting punished to the full extent of the law not because he killed the man, but because he didn't express any remorse for doing so?
There are a few things to unpack there.
Meursaults' origins are not made clear in the book, on purpose. The safest bet you can make is that he is the same as Camus, Algeria born, working-class colonial.
Camus uses the term "Maure" for the prostitute, which is to say "Moorish" but he uses the term "Arab" for the two men with the knife. So we cannot assume the Arab that dies is Algerian Arab, he may be a stranger. The term "Maure" as it was used when this book was published could potentially mean any Algerian, and Camus never felt the need to explain it further.
The killing, the crime, in The Stranger is meant to be ordinary. What is meant to be extraordinary and what causes Meursaults' death is that he is alienated from his life and his own defense. He isn't interested in his defense.
Camus made the point himself that the crime itself isn't what he was commenting on, he said Meursault dies because he clings to the truth, an inconvenient one for society (that he didn't particularly care about the death of his mother or this Arab), rather than modern hypocrisies, and that's what gets him killed, the truths we all ignore and repudiate to different degrees for the good of society.
So, when you ask, is it realistic, what exactly would be? A man uninterested in defending himself certainly will receive punishment. In the context of the book, yes, it is. But if your question is larger, say, would a white Frenchman who killed an Algerian native in Algeria with a credible motive to defend himself (remember, the Arab that get's shot has already used the knife on someone and he pulls it out when he sees Meursault, which causes him to pull out his gun) be punished, away from the context of The Stranger, then that is completely different.