Actually European defence technology is mostly home grown.

The reason being nationalism, and also the Americans refuse to sell us the latest stuff-- the only country that gets that is Israel (which then sells it to China ;-).  They won't even let British companies have it-- you know the people standing beside you in Iraq. (we are seriously talking about pulling out of the Joint Strike Fighter over access to the software).

It's inefficient, we run higher costs because we don't have your economies of scale and volume platforms.  The separate national fiefdoms bugger us. But we do have our own weapon systems technology (in some areas clearly superior eg conventional submarines, some forms of artillery and light armoured vehicle etc.).

We (UK) use your nuclear systems, but we were offered the chance to co-develop with the French, and went with the US.

Put it another way, there is no 'Europe' on defence, what there is is different nations of different force projection capability.  Its unsurprising the world didn't want the Germans to develop force projection (but they had the best armoured forces in NATO).

We don't spend as high proportions of GDP on defence, but then our labour costs are generally lower, too.  What we don't get is your economies of scale.

I don't think Europe is likely to get 'Imperial'.

I do think Europe is likely to strike its own deals with oil-producing states, not necessarily to the US's liking.

A lot of oil producers don't want to be dependent on the US alone, either as a customer or as protection.  Hence the Saudis buy their air force from us (the BAe Al Yamamah II project) not from the USA.

This has bearing on the Palestinian problem, and also Venezuela, amongst others.  Interests will diverge.

However I think Europeans of late, due to the anti-Americanism, take for granted the defense edge they have which is provided by American forces.

Anti-Americanism that is partially motivated by a different view on the effectivity of armed intervention. So I think the difference in strategical choices motivates the anti-US-sentiments rather than the other way around.

I'll also be really curious what Russian removal of resources will do to promote European hegemony under the EU banner.  I could easily see the EU becoming a LOT more Imperial once resource rich countries start looking after themselves, and all those diplomatic deals start to fall through.  What would a few cold winters or record breaking summers without steady energy do to motivate the EU towards militarism?  Ugly thought, but certainly not unthinkable.

Conquering and occupying an already much more militaristic Russia or parts thereof? Whoever thinks that would work, let alone yield a net energy benefit deserves to become history instantly. Besides, the Baltic and the Black Sea are very nice blockade points even without large forces.
In any case, for the foreseeable future (which is short) Russia and the EU have needs and abilities that are complementary. There's no use in rushing to make enemies.