My impression is that the European Union is too politically fractured to mount any consistent policy.
Just one example: the French government has made noises about doing something to counter the United States' extraterritorial application its sanctions regime. US sanctions against Iran effectively apply to European companies, even if they have basically nothing to do with the US. The US can unilaterally force the EU to stop doing business with Iran. The French see that as a violation of their sovereignty.
The problem is, if France proposes to do anything about it, Germany will object, because Germany fears that the US will retaliate against the German automotive industry.
Imagine if the US could only take action when 50 states all agreed. There's no powerful central government in Europe that can decide to temporarily sacrifice some interests in order to achieve something more important - establishing independence of action from the US on sanctions policy.