A French diplomat and the foreign ministry in Paris have confirmed the kidnapping of the woman who was well-known in the area where she spends much of the year.
According to witnesses, she was kidnapped on Manda island, just across a lagoon from Shela, an exclusive resort on Lamu island popular with the rich and famous. The circumstances of the kidnapping were not immediately clear.
Manda island is part of the Lamu archipelago on Kenya's Indian Ocean coast. It hosts a luxury hotel and was until recently considered to be one of the safest destinations in the country.
On 11 September, gunmen attacked a British couple in their fifties, Judith and David Tebbutt, on holiday north of Lamu. David Tebbutt was shot dead and his wife was captured. She is believed to have been sold on to pirates now holding her in central Somalia.
Somalia has been lawless for two decades after plunging into a bloody civil war with the 1991 ouster of President Mohamed Siad Barre.
Somali pirates frequently seize crew from merchant ships and pleasure craft in the dangerous waters off the conflict-ravaged Horn of Africa and have taken millions of dollars in ransom for their release.
A Briton kidnapped in southern Somalia in 2008, environmental researcher Murray Watson, is still missing. And a French secret service agent has also been held in Somalia for more than two years.
Tourism is an essential part of the east African country’s economy and has only recently recovered from the violence that had erupted after disputed 2007 polls scared tourists away.