Yes, indeed. Although on paper UK also joins this venture, they depend on USA for their nuclear arsenal (subs).
On the long-term, EU might need more nuclear weapons for adequate deterrence, and also FR might not be so stable given alt-right over there. So any integration needs to be stable on paper.
On the long-term, EU might need more nuclear weapons for adequate deterrence, and also FR might not be so stable given alt-right over there. So any integration needs to be stable on paper.