The VMF never built a modern amphibious assault ship. The closest they got were the three Ivan Rogov's, whice are really just jumbo LST's. The docking well is tiny, they must beach to do their work. The VMF lacks big utility landing craft as well. Their amphibious lift was purely tactical, available to be used in theater, but there was no strategic sealift or the ability to stage a big amphibious assault far from the USSR's or Russia's borders.
The Mistral class would give a very much improved capability to the Russians. The Mistrals are, however, built to commercial standards to save on cost, they are not built to military standards. This was a deliberate choice of the French. They will not have the same level of damage control or water tight compartmentation as a true warship.