Gaillard was born on June 13, 1974, in Paris. Her versatility as a cellist began to show itself during her education; she attended the Conservatoire de Paris, studying modern cello with Philippe Muller, chamber music with oboist Maurice Bourgue, and Baroque cello with Christophe Coin. She earned the conservatory's first prizes in all three fields. Gaillard also earned degrees in music teaching and musicology from the Sorbonne University. She has mostly been active as a chamber music player. In 1994, she founded Ensemble Amarillis with her sister, recorder player and oboist Héloïse Gaillard, and harpsichordist Violaine Cochard. Gaillard took third prize at the International Johann Sebastian Bach Cello Competition in Leipzig in 1998 and got a solo instrumentalist of the year nod at the Victoires de la musique classiques competition in France in 2003. In 2001, Gaillard made her recording debut on the Ambroisie label with an album of works by Britten. She performed with Baroque groups led by Christophe Rousset, Emmanuelle Haïm, and John Eliot Gardiner, and in 2005, she created the Pulcinella Ensemble, with which Gaillard remains associated. The group recorded the complete sonatas for cello and continuo of Vivaldi the following year on Ambroisie. Pulcinella Ensemble was renamed the Pulcinella Orchestra in 2013 and continues to perform.
Gaillard has performed and recorded an exceptionally wide variety of music that includes many Baroque chamber works, accordion-and-cello duo music (with accordionist Pascal Contet), Romantic repertory, and contemporary music. Most of her recordings have been of chamber music, but she recorded the cello-and-orchestra recital Dreams with the Royal Philharmonic Orchestra in 2010. Gaillard uses different cellos for her work in Baroque music (a 1737 Francesco Goffriller that was stolen from Gaillard at knifepoint in 2018 but then anonymously returned) and later repertory (an 1855 Bernardel instrument). She often performs with dancers and mimes.
As a recitalist and chamber player, Gaillard has appeared in England, Morocco, the U.S., Japan, and Latin America. Since 2003, when she began teaching at the Conservatoire de Musique et de Danse à Rayonnement Départemental in Aulnay-sous-Bois, France, she has had an important career as an educator. She has been a guest faculty member annually at the American Conservatory in Fontainebleau, and in 2014, she joined the faculty of the Haute École de la Musique Genève in Switzerland. Gaillard has continued to record, by 2022 issuing some 30 albums on Ambroisie and later Aparte. That year, she led Pulcinella on the album A Night in London with soprano Sandrine Piau and mezzo-soprano Lucile Richardot. ~ James Manheim, Rovi