Basically, yes. They can and will. That's real, proven, global power projection. The number of other countries in the world capable of that can be counted on the fingers of one hand.
What, with one ageing aircraft carrier?
The way you ask that question suggests that the answer should be "no"; but it's not. The answer is "yes".
No, it isn't. Libya is just across the Med from France, not in the Pacific.
> The number of other countries in the world capable of that can be counted on the fingers of one hand.
Well, really on one finger.
They didn't walk the resupply over. They have ships, they have friendly nations, they have the financing to purchase what they need, they have a real logistics organisation capable of resupplying globally. How inconvenient for this discussion that Libya wasn't on the other side of the planet, but there it is.
Well, really on one finger.
This is incorrect. Perhaps you're thinking of the USA, which is an order of magnitude more capable than any other. They are not, however, the only nation capable of delivering sustained global power projection.
Even for Falklands conflict, they barely managed to win, and that was with assistance from their friends vis-a-vis missile codes, satellite imagery, etc.
So they end up with one, again, if they even build it. Even the UK can do better than that, though admittedly the French carriers are at least notionally more capable than the crap Gordon Brown foisted on us.