You can be sure the US will be doing all it can to see Sarkozy elected in 2017. The primary will take place this November. Interestingly he just confirmed that he is indeed running again. The post-Brexit timing is (I think) noteworthy.
NATO will be around for the foreseeable future but the EU wants to expand its autonomous influence and power. Frankly they probably don't have the budget for what they're dreaming of, but it's clear there are many in the EU that view the Brexit as a window of opportunity... a moment in time in which they can act and the American toolkit will be somewhat limited.
For any players in the European elite who want to end US dominated Atlanticism... the hour has come.
Of course for the rest of Europe there is a sense of unease as a continent dominated by a waxing militaristic Germany is potentially taking shape. While no one would accuse Mutti Merkel of being a new Führer, there's still a lot of historical baggage.