What does it require that France does not have?
Logistics tail in depth, defense in depth. Air power projection at intercontinental/cross-ocean distances. Maybe I'm wrong, but I don't believe France has a ton of capability beyond reaching N. Africa, and some of it's islands and former colonies, or acting as part of a coalition like in Afghanistan.
But inherent in the idea is that "force projection", at least as I think the American media and political class considers the term, is a nation and it's military that's capable of action when opposed on a theater-wide basis, or by a peer-level military power, not just one that's trying to quash some asymmetrical warfare and insurgencies, or dealing with ;individual rogue third-world nations and failed states.
Although that particular assumption is untested, since obviously there hasn't been such theater-scale war or conflict since WWII, and despite the Cold War, other than proxy engagements, that buildup and deployment happened largely under peacetime conditions and open seas.
(although the Soviets certainly backed down when it became clear we were deadly serious and ready to go if need be during the Cuban Missile Crisis)