I would bet against any unified European action based on recent history and bet on "generally taking no action and leaving China relations to the member countries." This will almost certainly play to China's advantage as e.g. voters in France will ask why they aren't trading from China while Italy and Greece are benefiting from it.

Germany (the most powerful country in the EU) is particularly benefiting from trade with China, which also doesn't bode well.

I would love for it to turn out otherwise though.