France’s prime minister, Élisabeth Borne, sat on a recent, rainy evening in a dim room at a Red Cross shelter, listening to young women recount their personal stories of poverty, fractured homes and schooling struggles. She smiled reassuringly and asked piercing questions. But what she did not say was that she could relate. Ms. Borne’s youth was full of trauma. Her father survived Auschwitz-Birkenau, the notorious Nazi camp where one million Jews were killed, and died by suicide when she was 11. He left behind a bankrupted business and a shell of a wife. His daughter was taken under the...