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The young British actress was found dead at the 10th arrondissement apartment on Wednesday, two days before her 29th birthday.
A police spokesman said an autopsy had been ordered to determine the cause of death, adding that it appeared to be a suicide.
Speaking from the family home in Oxford her father, Richard Gordon, said: "She was a lovely, generous, unselfish person who gave her all for others and thought of others before herself.
"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."
Mr Gordon said his daughter loved playing her latest role of British singer and actress Jane Birkin in the upcoming biopic Serge Gainsbourg (A Heroic Life), adding: "She found the whole team and cast wonderfully creative and supportive."
According to Gala magazine, a friend of the actress burst into a nearby shop early on Wednesday morning calling for help.
The friend and the shopkeeper rushed upstairs in la Rue des Petites Ecuries to find the actress dead.
Friends said Gordon was deeply affected by the recent suicide of a friend in the UK.
In 2002 Lucy starred in historical drama The Four Feathers. The cast included Australian actor Heath Ledger, who died of a drugs overdose in his New York apartment last year.
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