Capony, a former librarian, was born in 1894, and was the fifth-oldest person in the world. She became France's oldest person in August 2006 after the death of the 114-year-old Camille Loiseau.
"She died peacefully from heart failure," her nephew, Rene Capony, said.
Almost blind and deaf, the woman had survived two world wars. Although she had never been married, she had once been engaged. However, her fiance died in 1914, and she remained single for her entire life.
The French centenarian had refused to enter a nursing home, and did not leave the house for 36 years, spending most of her time in bed surrounded by her nephews and nieces.
Capony never watched television as she didn't like the noise, though she found computers really amazing, her friends said.
Capony's death comes just a month after the then oldest person in the world, Japan's Yone Minagawa, died aged 114.
France's longevity record holder, also the oldest verified person in history, Jeanne Calment, died in 1997 at the age of 122.