Has a non-identical twin sister, Joy, who studied business and is married to an Italian count. Joy and her husband reside in Normandy where they rear horses.
Auditioned for the part of Tauriel in The Hobbit: The Desolation of Smaug (2013) and The Hobbit: The Battle of the Five Armies (2014) in 2010, losing the role to Evangeline Lilly. Her audition took place right after Benedict Cumberbatch's, who successfully obtained the role of Smaug in the films.
Before meeting Carla Bruni, French President Nicolas Sarkozy invited Green to join him on his campaign trail. She politely declined.
Stated her desire to work with fellow French compatriot Marion Cotillard.
Johnny Depp is one of her favorite actors and Tim Burton is one of her favorite directors. She worked with them on Dark Shadows (2012).