The 46-year-old was found beneath her flat in the city's wealthy 16th district on Wednesday evening.
Barry lived alone and anti-depressants were discovered inside her flat, which was locked from the inside, police said.
She was the daughter of British-born Birkin, best known as the muse and partner of late French singer Serge Gainsbourg, and British composer John Barry, famous for writing 11 James Bond movie themes including 'Goldfinger' and 'Diamonds Are Forever'.
Barry had studied fashion but turned to photography later. She had drug and alcohol problems which prompted her to open a centre for addicts near Paris.
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"Her fragility touched us," Filippetti said, adding that Barry was an outstanding photographer whose "sense of light and composition was very pictorial".
Birkin and John Barry, who died in 2011, separated in 1967, the year of Kate Barry's birth, and she was brought up until her teenage years by Birkin and Gainsbourg.
Kate Barry was also the half-sister of actresses Charlotte Gainsbourg and Lou Doillon.
Her photographs had appeared in leading French magazines such as Paris Match, Elle and Le Figaro and she had recently held an exhibition of her works entitled "Point of View. Portraits. Still Life" in Paris. She had one son, Roman, who was born in 1987.