Claire Gratton was born in Niort and began studying the cello with Sylvette Gaillard. She later graduated with distinction from the Poitiers and Bordeaux Conservatoires, where she attended Henri Demarquette's class. She also studied with Roland Pidoux, Xavier Gagnepain, Frans Helmerson, Patrick Gabard, Rainer Zipperling and Jaap Ter Linden.

She took an interest in early instruments and their repertoire, and obtained a diploma in Classical and Romantic performance practice with Philippe Herreweghe in Saintes. She was a finalist at the 2005 International Early Music Competition in Bruges and won First Prize at the Lyons Conservatoire in Claire Giardelli's class in 2006. She also studied with Bruno Cocset in Barcelona.

She plays with many ensembles, including Stadivaria, La Simphonie du Marais, L’Ensemble Baroque Nomade, Pulcinella, Le Concert d’Astrée, Le Cercle de l’Harmonie, Pygmalion and has taken part in numerous recordings.

She also enjoys chamber music, and is a founding member of "Il Convito", with her sister Maud Gratton and violinist Stéphanie Paulet.