What are the long term political goals of England, France and Germany?

Kissinger says in his book Diplomacy from 1994:

"For one of the most difficult lessons America has yet to learn is that nations cooperate for long periods only when they share common political goals, and that American policy must focus on these goals rather than on the mechanisms used to reach them."

If it is, like many think today, that the long term and common political goal in Europe are not further integration and solidification of EU at the current borders, but rather that the individual nations should mostly mind their own business, what are then the political goals of England, France and Germany? No one talks about this but they are negative about the EU.

A joker in this deck of cards is that there has been a suggestion that the Obama administration would be open for a Russia membership in NATO on a congressional hearing, something that Boris Yeltsin once argued for.

Does this mean that the US have given up on EU as a stabilizer and instead wants NATO to be the stabilizer of Europe including Russia? EUs success is of course extremely intimidating to Russia and this causes tensions. Russia has been talking about a new security pact for Europe themselves and it would perhaps be better if such a creation came from NATO than from Russia.