The Avel Vad was sailing with another vessel in the area between the Somali coast and the Seychelles when it was attacked at 0730 GMT on Saturday.
A skiff from a pirate ship began approaching "with aggressive intent", the French military said.
Soldiers aboard the tuna boat fired fireworks and warning shots at the pirates, scaring them off. They have not been caught.
Saturday's incident was the second time in less than a week that a ship from the CMB company, based in the north-west French region of Brittany, has come under attack from pirates.
European Union warships arrested seven suspected pirates after an attack on the Cap Saint Vincent 350 nautical miles east of Mogadishu on Tuesday.
Since last year a flotilla of foreign warships has been patrolling the piracy-plagued Gulf of Aden, one of the globe's busiest maritime trade routes.
Pirates have since redeployed to the Indian Ocean, a much wider area very difficult for naval forces to patrol effectively.
Since the start of October, subsiding monsoon winds have allowed pirates with small skiffs to resume their operations in earnest after a lull that had seen the number of hijacked vessels drop to two.
Among their latest catches are a British couple seized from their yacht, an Indian cargo ship, a Spanish trawler with a crew of 36, a Singapore container ship with 21 crew members and a Chinese bulk carrier with a crew of 25.
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