Attackers stormed the 288-foot Le Ponant as it returned without passengers from the Seychelles, in the Indian Ocean, toward the Mediterranean Sea, said officials with French maritime transport company CMA-CGM.
"This is a blatant act of piracy," Prime Minister Francois Fillon told reporters while on a visit to Brussels. "The Defense and Foreign Ministries are mobilized to act as quickly as possible, I hope in the coming minutes or hours to try to win the freedom of these hostages."
He did not elaborate. France has considerable military resources in the region, including a base in Djibouti and a naval flotilla circulating in the Indian Ocean.
A French frigate, Le Commandant Bouan, was temporarily diverted from its role in the naval arm of Operating Enduring Freedom to track the yacht, military spokesman Cmdr. Christophe Prazuck said. A Canadian helicopter on the HCMS Charlottetown was also taking part, he said.
The nearest U.S. ship is 100 miles away with Marines on board, reports CBS News national security correspondent David Martin.
The yacht was in the high seas in the Gulf of Aden, off Somalia's coast in the Indian Ocean, the French Foreign ministry said. At least some of the crew members are French, and no other nationalities were specified.
"French authorities are handling the situation," Jean-Emmanuel Sauvee, managing director of La Compagnie des Iles du Ponant, told reporters in the southeastern city of Marseille, where his subsidiary of CMA-CGM is based. The company did not want to comment further so as not to endanger the crew members held hostage, he said.
French military spokesman Prazuck declined to say what type of military operation might be planned, and said he did not know the exact location of the yacht.
According to the company's Web site, the three-mast boat features four decks, two restaurants, and indoor and outdoor luxury lounges. It can hold up to 64 passengers.
Le Ponant was next scheduled to carry passengers as part of a 10-day, 7-night trip from Alexandria, Egypt, to Valletta, Malta starting April 19. Prices started at $3,465, not including air fare or taxes.
Pirates seized more than two dozen ships off Somalia's coast last year.
Denmark's government paid a ransom to win the release in August of the crew of a Danish cargo ship that was hijacked by Somali pirates some two months after they were taken captive.
The U.S. Navy has led international patrols to try to combat piracy in the region. Last year, the guided missile destroyer USS Porter opened fire to destroy pirate skiffs tied to a Japanese tanker.
Wracked by more than a decade of violence and anarchy, Somalia does not have its own navy, and a transitional government formed in 2004 with U.N. help has struggled to assert control.
The International Maritime Bureau, which tracks piracy, said in its annual report earlier this year that global pirate attacks rose 10 percent in 2007, marking the first increase in three years.