The dead were named by Sud-Ouest newspaper as Jean-Pierre Micheaud from the western town of La Rochelle and Francis Servel from the southern city of Toulouse.
There were reports on Monday that another body has been discovered in the stricken vessel, bringing the number of dead so far to six.
News magazine Le Point was reporting on Monday that two French couples were still being searched for following the disaster.
Measuring 290 metres (950 feet) by 38, the Costa Concordia was carrying some 4,200 passengers and crew when it hit rocks just off the Tuscan island of Giglio on the evening of Friday the 13th.
Stricken luxury liner Costa Concordia may have been big enough to house swimming pools and restaurants but its very size might have complicated evacuation and rescue efforts, industry experts said
"What jumps out at me, is the size of this liner," said Jacques Loiseau, chairman of the French Association of Ship Captains (AFCAN).
The association had regularly tried to draw attention to the dangers posed by the tendency towards boats on such a massive scale, he said.
"Even in the best conditions, with such size, you'll never be able to save everyone."
But the ship was by no means the largest cruiseliner in use. Others can carry up to 6,000 passengers and 2,000 crew.
As travel companies opt for ever bigger vessels to cater to the needs of ever more passengers, authorities are increasingly concerned.
"The considerable increase in the number of passengers onboard the ships have led to new security and safety constraints," said the North Atlantic Coast Guard Forum of 20 countries in a document issued during a simulation exercise.
In case of an accident on such cruises, "the evacuation and the recovery of passengers will become very complex operations with a very significant risk of losses of human lives.
"In case of distress, it would be difficult for a single country to rapidly provide all necessary means of safety and an international exercise must not be ignored," it added.
In an exercise last September, the forum simulated a fire on a large ferry carrying 5,000 people between the north-eastern coast of France and a British port.
What was starkly clear was the complexity of evacuating thousands stranded at sea.
On sea, "we can evacuate 10 or 20 people by helicopter," said Atlantic maritime officials.
"But 2,000 or 3,000 passengers would be impossible," they added.
Beyond the sheer numbers of people, the Babel of languages spoken and diversity in cultures could further complicate rescue efforts.
"It is a determining factor in important times. A lot of training is required" to overcome this obstacle because panic hinders communication, said Loiseau.
"The instructions must be repeated in several languages used by passengers and, among the crew members, we often have problems finding the right words in such situation," said Loiseau.
The Costa Concordia was carrying 60 nationalities when disaster struck.