Rivet was born to an Alsatian mother and French naval officer father.[1] After the death of her father in 1910, she moved with her mother to Lyon.[1] She worked for a time in a hair salon before joining the convent of the medical sisters of Notre Dame de Compassion in Lyon in 1912. In 1933 she became Mère Marie Élisabeth de l'Eucharistie, the convent's Mother Superior.[2][3]
On March 24, 1944, she and her assistant were arrested by the Gestapo and taken to the Montluc prison in Lyon. From there, she was taken to Romainville, before being shipped to Ravensbrück concentration camp near Berlin, Germany. There, stripped of her religious garments, she was forced into hard labor. Rivet volunteered to go to the gas chamber on March 30, 1945, in place of a mother only weeks before Germany surrendered unconditionally.[5][6] She was 55 years old.