It's kind of funny to say that free trade is antithetical to the EU when economic integration and lowering barriers to trade were among the primary motivations for it (it was preceded by various economic agreements).
If you've your bucket of wealth full. You'll against the free market, which can transfer your wealth to other nations.
If you are a poor nation, you are more likely to try your luck after all what you can lose when you've nearly nothing.
Or if you are confident in your companies' methods of extracting wealth from other nation, then you are more likely to favor free trade.
Europe after imperialism was a bucket full of wealth and just wanted to shut off the door to prevent wealth from escaping.
Today, Europe's population is aging fast, plus they do not allow immigration. They just can't compete today!
Europe is in wealth preservation mode and American companies like Apple, Facebook, Google are superior at "value extraction".
Europe no longer wants to play this game and signals by enacting unreasbly difficult to comply with laws like GDPR.
There's even reactionary right wing movements claiming that immigrants are going to make everything go to hell.
You seem to have settled on economics as a zero sum game. Trade ministers in most countries haven't.
That's not how trade works. It's beneficial to both parties.
But not in practice. The biggest proponent of free trade, the US had been protectionist and only lifted trade barriers when its local industries got strong enough to compete globally.