In general, the produce you buy can be labelled “Produce of Country X” or “Made in Country X” if, and only if, 50% of the value added is added in Country X.
It’s a straightforward rule, but it has a couple of slightly surprising consequences:
There are plenty of products which can’t meet the 50% rule with respect to any country. They may be labelled “product of more than one country” or something similar.
With many processed food products, most of the value added resides in the processing. So crumbed, frozen fish fillets, for example, may be labelled “Produce of Country X” if the filleting, crumbing, freezing and packaging accounts for at least half the value, and took place in Country X, regardless of where the fish came from. Whereas if you buy fresh, unprocessed food labelled “produce of country X”, then the food almost certainly does come from Country X.
Words like “champagne” and “budweiser” may be labels of origin in one country, but not in another, so you need to check up on what they mean in your particular country, or else not rely on them in the assumption that they are labels of origin. The WTO does, I think, provide a forum through which disputes over such labels can be litigated internationally, so that a label of this kind is used consistently in different countries. But this forum does depend on somebody with an interest litigating the matter. And frequently the litigation gets selled by agreement between the parties, not always in a consistent way; as a result of litigation over the name “budweiser” the Anheuser-Busch product is sold under that name in the UK and Ireland, but elsewhere in the EU any beer sold under that name has in fact been produced in Budweis (and the AB product is sold as “Bud”). But unless you know the status of a particular label in your particular country, you can’t treat it as a reliable indication of origin.