Franklin received favourable notices for her portrayal of an unusually worldly teenager in the suspense film "The Nanny" (1965) starring Bette Davis. She also received an Emmy nomination for her supporting role in the TV movie "Eagle in a Cage" (also 1965) in which she again acted opposite Trevor Howard. She acted with Dirk Bogarde, who played her father in "Our Mother's House" (1967), a film that was nominated for the Golden Lion at the Venice Film Festival. Not long afterwards, Franklin played opposite Marlon Brando and Rita Moreno in "The Night of the Following Day" (1969) as the kidnap victim in the crime thriller. This was her first "adult" role, with one scene showing her topless. She appeared with Michele Dotrice in the horror thriller "And Soon the Darkness" (1970), a film that was remade in 2010.