The power projection is aimed towards maintaing their former African colonies where they still rely on to fund/subsidize a lot of social benefits and programs in France.
You also have Turkish people and pretty much everyone around the world able to join the French Foreign Legion which makes it very easy for the French republic to minimize political fallouts losing its citizens in Africa while able to deploy large armies consisting of non-French individuals fighting for French interests and sovereignty in the region.
WW2 was over long time ago. France is at the absolute vanguard of EU's offensive capabilities. After USN, perhaps only French Navy can compare as its own French owned vertical industries all come together to build up its standing army.
What do you think the Charles de Gaulle, Mistrals and FREMMs are for?
In more sophisticated words: France's naval forces are kinda weak and don't have power projection capabilities. You can't pretend to be a world power, if you don't have the force to back it up with.