The incident took place in the Gulf of Aden in September 2008.
A French navy team raided the vessel, Carre d’As, two weeks later, killing one captor and detaining the others.
A sixth man was acquitted. It is France’s first prosecution of suspected Somali pirates.
The prosecutors had asked for the men, now aged between 21 and 36, to be sent to jail for between six and 16 years.
They were charged with hijacking, kidnapping and armed robbery after seizing the boat and its crew.
They were accused of attacking the Carre d’As on 2 September 2008 and demanding a ransom of $2m (£1.3m; 1.5m euros) for the release of French couple Jean-Yves and Bernadette Delanne, both aged 60.
Leniency urgedA lawyer for one of the defendants said his client was a fisherman who had been forced to take part in the attack because he was a seafarer.
Another lawyer said the organisers of the attack were still at large.
Defence lawyers urged the court to show leniency, saying sentences of up to 16 years were disproportionate to the crime, as the Somalis did not have “blood on their hands”.
“This is the first time since the 18th century that this country has judged a case of piracy,” defence lawyer Cedric Alepee said, noting that the accused did not have “wooden legs, parrots on their shoulders or eye patches”.
The case was heard in a Paris court for minors because one of the defendants was a minor at the time of the attack.
As the trial came to a close, the defendants apologised to and exchange handshakes with the Delannes. One wished them long lives, while another asked for their forgiveness.
“Good luck,” Bernadette Delanne said.
Jean-Yves Delanne, who is known by the nickname Captain Haddock for his salty sea-dog appearance, said he thought justice had been done.
“I hope piracy is stamped out,” he said, “but this isn’t going to change the way things are. The West should do more to help.”
Somali suspects in three other French piracy cases are awaiting trial. Six men will go to court next May, charged in connection with the April 2008 hijacking of the luxury yacht, Le Ponant, and holding its crew of 30 hostage.
The International Maritime Bureau has said that better policing and improved security have reduced successful hijackings by Somali pirates this year.
Nevertheless, attacks linked to Somalia made up more than half the piracy incidents reported worldwide.