Schneider, who was just 19 when her performance opposite Marlon Brando caused outrage, died in Paris after a long illness.
French Culture Minister Frederic Mitterrand paid tribute to a "great artist" and to her "beauty, the detached irony of her look (and) the husky softness of her voice".
Credited with helping to introduce explicit sex to mainstream cinema, Schneider was a model when chosen for the role in Bernardo Bertolucci's film about a young Parisian woman who starts a sordid affair with a middle-aged American businessman.
The graphic sex scenes led to the film being banned in several countries.
Schneider accused its star and director of exploiting her, saying she felt humiliated and "raped" by the "butter scene".
Schneider and Brando did not speak for some time after, but they were friends until his death. She later said: "Undoubtedly, my best experience about making the film was my encounter with Marlon."
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Expressing your creative side is strongly advised. Take this opportunity to write, paint or play music. Relatives may not appreciate your work, but that doesn't matter. The important thing is to satisfy your own taste. People who are daring and experimental will appreciate your efforts. Don't be surprised if you're given a chance to showcase your work in a magazine, boutique or gallery. Fame and acclaim can be yours, so long as you're willing to follow your instincts.More