Vivien Leigh's ancestry is highly disputed and unknown. During GWTW, Selznick, the producer, said, "Scarlett O'Hara's parents were French and Irish. Coincedentally, Miss Leigh's parents are also French and Irish."
Vivien Leigh was born Vivian Hartley, in India. Her father was a cavalry officer serving in British India. His ancestry is undisputed, as he is of well-documented Yorkshire blood. It is her mother, Gertrude Mary Robinson Yackje, from which the mystery arises.
Gertrude claimed she was Irish, and with Christian names like "gertrude" and "mary" it is believable, but her last name creates issues. Yackje is not French or Irish, or even European. There have been Yackjes (also spelled Yackjee) in Bengal, India, and so it speculated that Gertrude was part-Indian. This is the generally-accepted reason for Vivien's stunning Eastern beauty, and it is possible that she may be Afghani (Yackhe being an Afghan village), but she is more well-known as being Anglo-Indian, and Anglo-Indian sites list her. Anglo-Indian means to have British/Irish blood and Indian blood. It, then, was a race shunned by both English society and Indian society.