Born in Montpellier, in southern France, Jeanne Demessieux was the second child of Marie-Madeleine Demessieux (née Mézy) and Étienne Demessieux. After taking private piano lessons with her elder sister, Yolande, Jeanne entered the Montpellier Conservatoire in 1928. 4 years later, she obtained 1st prizes in solfège and piano.
In 1933, she began her studies at the Paris Conservatoire; studying piano with Simon Riera and Magda Tagliaferro, harmony with Jean Gallon, counterpoint and fugue with Noël Gallon, and composition with one of Franck's youngest pupils, Henri Büsser. The same year, she was appointed titular organist at Saint-Esprit, a post she held for 29 years.
Between 1936 and 1939, she studied organ privately with Marcel Dupré, whose organ class at the Conservatoire she joined in 1939. After receiving a first prize in organ performance and improvisation in 1941, she studied five more years privately with Dupré in Meudon, before she played her début recital at Salle Pleyel in Paris in 1946. This was the beginning of her career as an international recitalist.
Altogether she gave more than 700 concerts not just in France, but also in the United Kingdom, Belgium, the Netherlands, Switzerland, West Germany, and the United States. Blessed with a prodigious memory, she knew more than 2,500 works by heart, including the complete organ works of Bach, Franck, Liszt, and Mendelssohn, as well as most of Dupré's compositions for the instrument. A prolific recording artist, she received in 1960 France's Grand Prix du Disque Award for her Franck intégrale, committed to disc two years before.
In 1962, Demessieux was appointed titular organist at La Madeleine in Paris. She combined this with serving as professor of organ both at the Nancy Conservatoire and later at the Conservatoire Royal in Liège. Increasingly poor health obliged her to limit her performance activities after 1965. She died in Paris on 11 November 1968.