France invited large amounts of immigrants from Africa to help rebuild so it’s not like they didn’t see immigration.
I think there are two main reasons that the poorest parts of the population are stagnating. One is poverty traps, and especially multi generational poverty traps are very hard to escape. Another is geographic location. Americans dont move as much as they used to, all around the world poorer people move to areas with more jobs and opportunity but today mostly richer people move and poorer people stay put in areas that are impoverished.
Immigrants largely don’t come with a set geography or generational poverty weighing them down which is why their kids do so well.