"The contacts through which the French government was seeking to obtain the release of Marie Dedieu, held in Somalia since October 1th, have announced her death, but we have not been able to determine the date nor the circumstances," the foreign ministry said in a statement.
"Mrs Dedieu's state of health, uncertainty over the conditions of her detention and the fact that the kidnappers probably refused to give her the medication that we sent her lead us to believe that this tragic outcome is unfortunately the most likely," the ministry said.
A gang of 10 armed men seized Dedieu, 66, from Manda Island in Kenya's Lamu archipelago earlier this month and fled by sea to Somalia, fighting off an attempt by Kenya's navy to stop them.
There had been serious concern over the health of Dedieu, who was wheelchair-bound after an accident several years ago and required medication every few hours.
The ministry said it had informed Dedieu's family of her death and was demanding the unconditional return of her remains.
"The French government expresses its profound shock, great sadness and solidarity with the family and loved ones of Marie Dedieu," it said.
"It also expresses its indignation at the cruelty and complete absence of humanity shown by our compatriot's abductors, whom we want to see identified and brought to justice."
Kenyan officials said they suspected Somali Islamist Shebab insurgents had carried out the abduction, but sources in Somalia dismissed the theory.
Dedieu had lived for 15 years in the Lamu archipelago, off Kenya's northern coast.
Her kidnap was the second in the area in less than a month and dealt a further blow to Kenya's tourist trade after France and Britain warned travellers to avoid the Kenyan coastline near Somalia.
A British tourist, Judith Tebbutt, was seized to the north of Lamu and taken to Somalia on September 11 by an armed gang who killed her husband. She is believed to have been sold to pirates now holding her in central Somalia.