Bresson was born as Marie-Louise Herbulot on 15 March 1913 in Mascara, Algeria (then French Algeria). She attended school in the coastal city of Oran. She became a teacher at the age of 20; her first class was one with 40 pupils. Her main subjects were maths, spelling, history, and geography. She learned to read and write in Arabic but did not speak it.

In 1962, after the end of the Algerian War, Bresson emigrated with her parents to France, settling first in Toulouse, before spending a year in Perpignan. She looked after her mother, Lina, who lived to be 100 years old. In her later years, she enjoyed crocheting, embroidery, knitting, and painting. She had an operation to remove cataracts aged 90, and she stated that it was her first blood test in her life.

Bresson fractured her femur at the age of 104 and moved into a nursing home shortly thereafter. As a supercentenarian, she is reported to be in good health, still completing crosswords and watching quiz shows on television. She reads frequently, romance novels in particular, without glasses. Her sister was still living as of 2022 at the age of 99.