The Russisns have significant air already on Syrian airfields and could fly in more with little trouble. This flotilla thing is a PR stunt for a photo op of Russian naval power. To be honest if the Frogs and the EyeTies decided to put an end to this flotilla right now they could do so. The Kuznetsov was a badly designed vessel 30 years ago when she was the Riga or was that Tiblisi, so many name changes. And this is like her 4th cruise to the Med in recent years but people are getting worked up. She really adds little to Russian capability in Syria and is little threat to French, Italian or even Spanish naval forces.
Regardless of politics, that technology is not impotent when it carriers fighters that are more advanced. To discount them, you risk at your own peril.
Her 12 P-700 Granit cruise missiles are a significant threat to all aforementioned naval forces including ours especially if they are nuclear tipped. The Russians could also have one or two Oscar II submarines hanging around which is armed with 96 P-800 Oniks Yakhont (Super Sunburn) missiles which could cause horrific damage.