France had gone ahead with the sale of two Mistral warships to Russia, despite calls from NATO and the United States to hold off on the €1.2 billion ($1.6 billion) deal over the crisis in Ukraine.
During their training, the 400 sailors will be staying onboard a Russian ship docked behind one of the two Mistral helicopter carriers.
France agreed the sale under a 2011 contract, with the first vessel due for delivery in October and the second in 2015.
The Mistral, the second largest ship in the French navy, is a high-seas military base that can transport up to 16 helicopters, four landing craft, 60 armed vehicles and some 700 troops.
France has said it is leaving the door open to re-examining the $1.6 billion contract in October, when the first warship is scheduled for delivery to the Russian fleet.
Since Russia's annexation of the Crimean Peninsula, Washington has voiced repeated objections to the deal, but Russia has stressed that France would face heavy penalties if the deal is scrapped.
"We have regularly and consistently expressed our concerns about this sale even before we had the latest Russian actions and we will continue to do so," Assistant Secretary for Europe Victoria Nuland told US lawmakers ahead of a visit to Washington by French Foreign Minister Laurent Fabius in May.
US lawmakers also pushed for France to halt the sale, saying it would be a clear sign of global anger at what they said was the "aggression" of Russian President Vladimir Putin toward Ukraine.
"If we increase NATO defense spending while joining in a coordinated embargo on all arms sales to Russia, including halting the sale of two French-built Mistral amphibious ships, it will send a clear message to Putin that he will not be allowed to trample on the rights of his neighbors," Congressman Eliot Engel, a Democrat, told the House Foreign Affairs committee.
"I'm not here to bash the French, but I think this is a time when the French could stop that sale from happening and send a very strong message to the Russians," added Republican lawmaker Adam Kinzinger.
But French officials reacted with astonishment, denying that US officials had expressed worries over the contract.
"The United States, like the Europeans, have never voiced privately any concerns about this," a French government official told AFP, asking not to be identified.