Buying a ship is one thing, actually being able to use it is another. They had some larger scale ship-borne helicopter experience with their Moskva-class cruisers and Kiev-class carriers but they were primarily used for anti-submarine warfare, not the assault role. The complexity of heli-borne and seaborne assaults from a ship is not as easy as the Marines may make it seem to outsiders and I think the Russians will have a difficult time with making it work for a while, if ever. It may be a nice showpiece for a while but I don't see it having a big impact.
One thing it does show is how far the Russian Navy has sunk from it's Soviet-era peak in the 80's. It is pretty pathetic that they have to turn to one of their former foes to first build them a ship then give them plans to make more. Almost all of their seagoing ships are going to run out of life soon and they don't have anything to replace them with. All they have built since the fall of the USSR is a few frigates and a few subs, hardly a world class navy by any standards. Even their modification of the old Kiev-class carrier Admiral Gorshkov into the INS Vikramaditya has been plagued by cost overruns and serious delays of several years, it is so bad that it has strained the Indian-Russian defense relationship.
I am a little surprised this sale is happening (but hey, it is the French) but overall not much too worry about, except for maybe Georgia, they have plenty to worry about anyways without this new threat.