...whereas three years of service in French Foreign Legion allows you to apply for citizenship, or immediately after you are wounded in battle ("French by spilled blood")
Serving in the Foreign Legion is not like 'being in the military' in other places...
Indeed no... Légion étrangère is very often front-line, opex, desert, jungle... A very special and strange military corps that meddled with politics in the 1960s...
https://en.m.wikipedia.org/wiki/Algiers_putsch_of_1961
And nowadays they select at the entrance.