La Somme "was probably taken for a commercial ship by the two small skiffs" some 250 nautical miles off the coast of Somalia, said Prazuck.
"They understood their mistake too late," Prazuck said.
One skiff fled, and La Somme pursued the second one in an hour-long chase.
"There were five suspected pirates on board. No arms, no water, no food," Prazuck said.
France is a key member of the European Union's naval mission, Operation Atalanta, fighting Somali pirates in the Gulf of Aden. It has aggressively tracked and caught suspected pirates and handed over at least 22 to Kenya. An additional 15 suspects were brought to France for prosecution after allegedly seizing French nationals' boats.
President Nicolas Sarkozy called for tougher action against piracy last year after dozens of attacks.