I don't think a common language is as necessary as you are making it out to be. India uses English as lingua franca because it has dozens on languages, and it is a more or less cohesive country.
And the US would love for the EU to defend itself. It's a large part why the U.S helped rebuild after WWII, and why the US has been begging NATO members to contribute the 2% GDP they promised for years. A strong EU is spelled out in U.S foreign policy.
Then the US shouldn't have over decades worked to undermine EU defense industry.
I trust actions more than words. The US over the decades did all it could so that EU did not, in fact, stepped up its defence, mainly for its own damn interests. A Europe that depends on the US to shoulder part of its defense is a Europe a lot more susceptible to US interests.
I am actually glad this should be coming to an end. I always thought EU should get rid of US influence.
In that sense, European countries were never as close as they are right now. I expect it to strengthen as time passes, especially now that the US should be seen as an hostile foreign nation to every European country.
Not to mention that after the shitshow that Brexit proved to be, even right-wing parties in Europe sort of abandoned their "leave EU" rhetoric.