Many French first ladies went by one of their middle names rather than their given name. There have actually been 4 who were born with the given name Jeanne, but only 3 retained it.
19th Century
Élise Thiers (born Eulalie Élise) 1871–73
Élisabeth Charlotte Sophie de Mac Mahon 1873-79
Coralie Marie Louise Eudoxie Grévy 1879–87
Cécile Carnot (born Marie Pauline Cécile) 1887–94
Hélène Casimir-Perier 1894–95
Berthe Faure (born Marie–Mathilde Berthe) 1847–51
Marie–Louise Loubet 1899–1906
20th Century
Jeanne Fallières 1906–13
Henriette Adeline Poincaré 1913–20
Germaine Deschanel (born Camille Armande
Marie Germaine) 1920
Jeanne Victorine Julienne Marie Millerand 1920–1924
Jeanne Marie Louise Doumergue 1931
Blanche Doumer 1931–1932
Marguerite Lebrun (born Jeanne Emilie Marguerite) 1932–1940
Michelle Auriol 1947–1954
Germaine Alice Coty 1954–1955
Yvonne Charlotte Anne Marie de Gaulle 1959–1969
Claude Jacqueline Pompidou 1969–1974
Anne-Aymone Marie Josèphe Christiane
Giscard d’Estaing 1974–1981
Danielle Émilienne Isabelle Mitterrand 1981–1995
Bernadette Chirac 1995–2007
21st Century
Cécilia María Sara Isabel Attias 2007
Carla Gilberta Bruni-Sarkozy 2008–2012
Source: French Wikipedia: Liste des Premières dames de France