A gang of 10 armed men seized Marie Dedieu this month from her home on Manda Island, prompting a sea battle between Kenyan forces and her abductors.
Kenyan officials sent mediators into Somalia a day later to negotiate her release.
Dedieu lived in a luxury home on the scenic Lamu archipelago for about six months out of the year. Kenyan officials and an acquaintance said the woman, in her 60s, used a wheelchair and was not in good health.
"The contacts through which the French government was trying to release Marie Dedieu ... have announced her death," the ministry said in a statement, adding the date and circumstances of the death cannot be specified.
The ministry said Dedieu's death "is almost sure" even if it does not have her body.
"She was an ill and disabled woman," Foreign Minister Alain Juppe said. "This is therefore a deeply barbaric and violent act. France condemns firmly this act."
"Marie Dedieu's health, the uncertainty about the conditions of her detention, the fact that the abductors had probably refused to give her the medication we had sent her, make us think that this tragic end is unfortunately the most plausible one," the ministry statement said.
Dedieu's friends and relatives have been notified, it said.
"The French government wants to say that it is deeply moved, saddened and that it supports Marie Dedieu's relatives," the statement said. "The government also wants to express its indignation following the complete lack of humanity and cruelty from the abductors of our compatriot. We want them to be identified and brought to justice."
The statement said the government is requesting "the repatriation of our compatriot's body."
The Kenyan government sent its condolences to Dedieu's "family, friends and colleagues" in a statement Wednesday.
"The kidnapping and detention of Marie Dedieu was a terror act not only against her, but also against Kenya, her home country France and the entire world," the statement said.
"... The Kenyan government thanks the French government and the people of France for their continued support even during this moment of loss."
Dedieu's abduction was the second in the area in a month, a major blow to Kenya, which relies on tourism dollars.
Gunmen seized British tourist Judith Tebbutt and killed her husband near Lamu last month. Security analysts have said Tebbutt is being held by pirates in a remote corner of Somalia. British government officials have asked journalists not to reveal her exact location to avoid abduction attempts from rival gangs.
France and Britain warned travelers to avoid the Kenyan coastline near Somalia in the wake of the abductions.
Kenyan officials have said they believe the kidnappings are carried out by the Al-Shabaab Somali militant group. A third incident involved the kidnapping of two Spanish aid workers at the Dadaab refugee camp last week.
Kenyan forces crossed into Somalia this week to pursue the militant fighters after the kidnappings heightened tensions in East Africa.
In the statement Wednesday, the Kenyan government said operations against Al-Shabaab were continuing.
