France considered Algeria as an integral entity within the country. When Algeria was absorbed by France in 1848, 3 departments were made in Oran, Algiers, and Constantine. From then on, France began assimilating Algeria into France, culturally (proposing assimilation policies for native Algerians), politically (departments), and invited their own citizens, as well as others, to live in French Algeria (Pied-Noirs). This fanned the flames for Algeria to break away from France as soon as possible, even though France implemented less stricter policies (Algerians were all French citizens from decree in the mid 1940s).
When war came, the battle lines were drawn, and it felt like a war among people. It broke Algeria, and after a long struggle, the nation had its independence in 1962, and the Pied-Noirs, prominent French citizens, and others left Algeria for their homeland.
You've answered your own question: Because Algeria in the mind of the French governments before and during the war was part of France in every single way. Algeria just wasn't a colony like Indochina or any other of their overseas colonies, Algeria was as French to France as Brittany or Normandy. This is the mindset we have to think of if we are going to consider why France kept the war in Algeria going until 1962. Why would France give Algeria independence when if faced with the same situation in Limousin, the exact sort of repression would happen?
I'm willing to elaborate on this, but I feel like you've already answered your own question. Perhaps there is something more specific you'd like to know?