Yes. And I can tell you, as someone living in such a country, they're extremely hostile to the non-EU countries. And typically involve respecting EU naming rules (can't call it champagne!), food products held to much higher standards than EU manufacturers, and quotas.
Held to higher standards than EU manufacturers? That would be odd. The point is that in order to sell on the EU market, you have to meet the standards of the market.
> "they're extremely hostile to the non-EU countries"
Can you give me one example?
As for Champagne, its a product from the Champagne region of France (similar to how Prosecco is from Italy), I don't see why it's a problem to call similar products from elsewhere sparkling white wine.
If you're referring to Champagne, then the answer is to build up your own brand. If I was in the drinks industry and produced cola, I don't have the right to sell it as Coca Cola. It's the same thing with Champagne.
> "It will probably also have to allow in EU exports which could threaten parts of their economy."
Of course they'll have to let in EU exports, just like the EU will have to let in UK exports. Why? They're all members of the World Trade Organisation.
The EU is set up to allow the member countries to cooperate more closely, through lower trade barriers and suchlike. The idea that leaving the EU means zero trade is absurd.