In return, France is vying for a bigger chunk of Russia's oil and gas business.
The contentious issues were discussed between Putin and French President Nicolas Sarkozy during a visit by the Russian government leader to Paris on Friday.
No breakthrough was announced on either side but the French president's office said both leaders agreed that a "a pending deal to build four Mistral-class warships would be a 50-50 project."
If clinched -- along with rights to construct several other vessels of the same class in Russia -- the deal would mark the most important transfer of military equipment to Russia by a NATO member country.
Designed to attack the shore from the sea, the Mistral class is viewed as an ideal weapon for Russia against possible uprising by nearby countries.
Aside drawing pressure from those neighboring states and the United States, the potential contract faces serious obstacles of its own.
France 24 reported that Moscow was adamant on its conditions for the transfer of technology and the building of such vessels on Russian soil.
"Paris has refused this condition and has stipulated that construction takes place in France," the French news medium reported.
"The world is going through a difficult time and we have to stand together to remain competitive," Putin was quoted saying by French media on Friday. "In scientific and technological areas, we must unite our efforts," he said before entering talks with Sarkozy.
The Mistral amphibious assault ship can carry 16 heavy or 35 light helicopters, dozens of tanks and more than 900 soldiers.
Russia owns only one Soviet-built aircraft carrier, which is much smaller than its U.S. counterparts and is considered outdated.
After boosting Russian trade with Germany and Italy, France has become Putin's latest trade endeavor. Likewise, Sarkozy is set to visit St. Petersburg next week to attend a major economic forum.
It was reported that French energy companies EDF and GDF-Suez were also involved with Russian energy companies to an attempt to participate in Russian pipelines North Stream and South Stream, "at the expense of participation in the European project, Nabucco."
France's Total SA oil giant is also said to have submitted a bid for between 20 and 25 percent of the Yamal gas field in cooperation with Russian company Novatek. The bid was also at the center of Putin's talks with Sarkozy.