In 2005, surgeons gave her a new nose and mouth after she was disfigured by her pet dog.
But heavy use of immunosuppressant drugs weakened her and she succumbed to cancer in April at the age of 49, the BBC’s Hugh Schofield in Paris says.
News of her death, announced by a hospital in Amiens, was delayed to respect her family’s privacy.
She told the BBC in 2009 that when she looked in the mirror she saw a mixture of herself and the donor. “The donor is always with me,” she said.
Figaro newspaper said she had suffered another transplant rejection. The strong anti-rejection treatment she was receiving led to two cancers, it added.
In her BBC interview she said her disfigurement by her dog had come as a result of an attempt to end her life.
After taking an overdose of sleeping pills, she awoke lying beside a pool of blood, with her pet Labrador at her side. The dog had apparently found her unconscious, and desperate to rouse her, had gnawed away at her face.
The injuries to her mouth, nose and chin were so extreme that doctors ruled out a routine face reconstruction. Instead they proposed a ground-breaking face transplant.
She was happy with the surgery but expressed distress at the attention from the media and passers-by that the operation brought her.
In recent years, face transplants have been performed in several countries, including the US, Spain, Turkey, China and Poland.