A source close to the probe, speaking on condition of anonymity, said four people had been on the yacht, now being towed to Djibouti where "suspicious marks" are to be studied by agents of France's DGSE spy agency.
Foreign ministry spokesman Bernard Valero said the crew issued a mayday signal, but by the time the frigate Bayern arrived the crew had disappeared.
"Following the alert from the crew, we asked our German partners to send one of their ships taking part in Operation Atalanta," Valero said, referring to the EU anti-piracy mission off Somalia.
The 5,600-ton German warship found the yacht, but "no-one was on board and we have no certainty about how many people had been aboard nor what may have become of the crew of the catamaran."
Atalanta spokesman Commander Harrie Harrison told AFP that the operation was "investigating and trying to work out why the yacht was empty.
"The next of kin details are yet to be confirmed, and we're obviously waiting for that confirmation. We're monitoring and doing what we can," he added. The German defence ministry had no further details.
A Yemeni coastguard official said two yachts with a total of six French citizens aboard had entered Yemeni territorial waters on August 19th and had left on September 4th.
The official, who also asked not to be named, said he had heard that "international forces on Friday found one of the two yachts off the coast of Ras Sartak" near the border with Oman.
While officials would not speculate on the fate of the missing crew, the waters between Yemen and Somalia are notorious for attacks by pirate gangs, and French yachts have been among the vessels seized in the past.
On Wednesday, Denmark announced the release of a Danish family more than seven months after they had been kidnapped by Somali pirates. A maritime monitoring group and local sources said a large ransom had been paid.
A British couple, Paul and Rachel Chandler, were seized by pirates in October 2009 as they sailed from the Seychelles to Tanzania and were held for around 13 months.
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 ransoms for their release.
According to the watchdog Ecoterra, at least 50 vessels and at least 528 hostages are currently being held by Somali pirates, despite constant patrols by warships from several world powers.
A French couple was kidnapped from on board a yacht in September 2008 as it headed through the Gulf of Aden. A ransom was paid, but French commandos later ambushed the pirates, killed one, captured six more and recovered the cash.
In April 2009 another French yacht was seized. This time special forces troops intervened when the boast was still at sea. In the ensuing gunbattle a French bullet accidentally killed the hostage skipper.
In addition, a French DGSE agent is thought to have been held hostage by Islamist militants in the Somali capital since July 2009.