What does the reference to "a soldier" tell you about the time period of the story?

The reference tells us that the story is set during wartime. Specifically, it is set in French Algeria during the Second World War. France had been speedily conquered by German forces, and a large part of the country came under their direct control. The rest of the country was placed under the authority of a puppet regime based in the spa town of Vichy. The new regime was racist, authoritarian, and reactionary and maintained control over French Algeria. Prejudice and bigotry towards France's Arab colonial subjects were widespread, leading to the development of a growing resistance movement.
Official discrimination against the indigenous population provides a background against which the main action of The Stranger unfolds. Meursault shoots and kills an Arab without the slightest compunction; the violent pimp Sintes beats his Arab girlfriend and generally treats her with contempt; and when Meursault is finally brought to trial for the murder he's committed, his lack of concern for his late mother appears to have more significance for the court than the life of an Arab.
The Stranger does indeed take place during wartime, as already mentioned. But there are a number of wars running throughout the story—seething, undeclared conflicts that change the lives of those concerned more completely than the more formal conflict raging in the background.