I agree with your premise. What the French see is not a EU without the "Frenchity" as you put it, but rather a French EU, where everyone else would give up their Germanity, Italianity... For some reason, unknown to me, the Germans seem fine tossing out their Germanity in exchange for French, but the other nations aren't going to take it any more.
That's about to change, and rather radically I fancy. Once Shoe-odor and the Greenies are booted out of power in a couple of months (they rate to be absolutely clobbered, btw), the new gov't won't be nearly so cozy with either the froggies or the Russians.