Sure, might be challenging to project that power to the straight of Taiwan, but by no means impossible as part of a coalition force. And especially the French have some vested interesst in the Pacific with their overseas territories.
I'm not sure the Italian carriers are relevant for operations in Southeast Asia. Maybe once they get F35Bs, but their Harriers would not fare well against much of anything, and that's assuming they have the ability to operate at such a distance from the Mediterranean in the first place. (Incidentally, what most of the world calls a carrier is not what the USN calls a carrier. STOVL carriers are not really in the same class as CATOBAR carriers!)
True so that US carriers, and vessels like the De Gaulle and the British carrier (Elizabeth-class if memory serves well) are different beast than the Italian ones. And the US has quite a few of those.
China will be hindered by not having any real allies, other than short term allies of convenience (Iran, Eritrea, for example).
The Japan Maritime Self-Defense Force is much more impressive than the Brits and the French though. (And Japan has major strategic reasons to keep the Chinese on the far side of the Taiwan Strait, most relevant being that that's the easiest place to stop an island hopping campaign towards the home islands)