He said that about a dozen pirates seized the vessel and that around 20 of the 30-strong crew were French, and the rest were Ukrainians.
Christophe Prazuck, a spokesman for the French armed forces, said the ship was "hugging the eastern coast of Somalia" and was "being constantly followed" by a French naval vessel.
"It is observing what is going on board the Ponant and is showing that we are present and constantly following what is happening to our nationals."
Late on Friday, Francois Fillon, the French prime minister, said the defence and foreign ministries were working to obtain the release of the hostages, adding: "We have relatively large military means in the area."
France maintains its largest foreign military base in nearby Djibouti.
The 32-cabin yacht, Le Ponant, was sailing between Somalia and Yemen when it was boarded by pirates on Friday.
According to officials from the CMA-CGM, a French maritime transport company that owns the ship, there were no passengers on board at the time.
Amid the absence of a functional government and continued conflict since 1991, pirate attacks are frequent off Somalia's 3,700km coastline.
While Somali pirates have mostly targeted cargo vessels, a boat carrying some 600 European tourists narrowly avoided being boarded in November 2005.
"You're looking at a powerful maritime mafia," Olivier Hallaoui, from French security specialists Secopex, said.
"Most are fishermen-turned-bandits, with links to clans, local militias who realise this is a lucrative business because in almost every case ransoms are paid."
Pirates seized more than two dozen ships off Somalia's coast last year.
It has prompted the international maritime bureau to advise sailors not to travel closer than 200 nautical miles to its shore.