If needs be. They ran a ferocious pace of sorties for an extended period from off the coast of Libya a bit under a decade ago, and since then it's not exactly been sitting on the sidelines; the aircraft, the carrier, the weapons and the logistics. That experience is still present in the personnel, the carrier is still operational, they've still got the air power to go with it.
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".
Libya is just across the Med from France, not in the Pacific.
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.
No. A very local war against a 3rd world country who almost beat us. A few more Exocet strikes and the task force would have been out of the game. If we now went to war using our bloated and incompetently designed new carrier, against a 2nd world power (say Russia, China, or even, dare I say it France) the thing would be at the bottom of the ocean in short order.
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".