The United Kingdom; The European Union; NATO: which is the primary sense of identity?

[Brenus]

Well, a lot of questions.
I will try to answer some of them as a former French professional soldier.
First I don't think Trump will dissolve NATO as it is a good tool for US supremacy and it sell a lot of US weapons to the "allies". What Trump wants, as he said during his campaign, is US first, so the demand of an increasing budget from the Allies is just in order to buy more US equipment.

As a French, our defence is based on the horrible but efficient concept of dissuasion which means that any country attacking France will be vaporised by nuclear weapons. No proxy wars, no limited war, just war.
French projection capacity in Africa and others parts of the world where the French interests are in danger or concerned is covered by the Army, Fleet and Air Force which are (allegedly) enough for the job (i.e. Chad), big UN missions being done in cooperation with others countries (Iraq first Campaign being an example).
As a French, I think we have to be independent of others countries interests. It is not possible to use the French Nuclear firepower to protect Norway... Cooperation is possible, not subordination.
Unfortunately, under Sarkolland, France was reunited to NATO, and our capacity in making our own weapons system badly damaged.
Fortunately, with Trump demands and his comments about NATO, perhaps some European Nations having lived under the dream of the US umbrella will realise that is was just this, a dream, and start to think about building their own forces.

The EU is dead. Built as a political project it was killed by the Commission and it undemocratic political behavior, the spreading of poverty and the choice of an economical model which can't be challenged by democratic votes, by law under the actual Constitution.
EU has no respect or acknowledgment local history or traditions. Having an unique model, the EU leaders are not able to see they just go to the wall.

The French identity, as I am concerned, and some French might disagree, is based on a political contract based on the French Revolution (1789). The french Identity can not be based on territory, as it had changed, and the longest French border is with Brazil. This fact rules out "culture" as well.
It can't be based on language as a lot a French speaking are not French citizens (Quebec coming immediately in mind, but some in Louisiana as well). 29 countries have French as official languages.
It can't be based on religions, as France has all of them, and a majority being atheist.
It can't be based on ethnicities as well, for obvious historical reasons.