Gordon, who would have turned 29 on Friday, appeared in a dozen films, including as reporter Jennifer Dugan in "Spider-Man 3." She portrays British singer and actress Jane Birkin in an upcoming biopic about Serge Gainsbourg.
Gordon's father said the death was a "complete shock."
Speaking from the family's home in Oxford, Richard Gordon told Britain's Press Association that his daughter was "a natural actress all her life, since she was about 2."
"She's always loved being on stage and in front of the camera and she has kept all her naturalness and charm all the way through. She has been the most beautiful daughter. We are obviously devastated."
He said she loved her latest role, in the Gainsbourg film, and thought the cast was "wonderfully creative and supportive."
He added that his daughter spent much of her childhood and her summer vacations in France and was bilingual. She recently moved to Paris after living in New York.
Gordon's agents did not return phone calls seeking comment Thursday.
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