Green is a natural dark blonde she has dyed her hair black since she was 15 years old. Life and cinema don't have borders.' Green has described her family as 'bourgeois', and has said that her sister is very different from her.
However, she was raised without religion she has said 'I feel like a citizen of the world. Her mother, a pied-noir, was born in Algeria (during that time, Algeria was part of France), later moving to France.
Her father is of Swedish and French descent, and through him she is the great-granddaughter of the French composer Paul Le Flem. She is the daughter of Marlène Jobert, an actress, and Walter Green, a dentist. Green was born in Paris, France, two minutes earlier than her fraternal twin sister, Joy (Johanne).
