Sure, the agreements say that whatever is imported needs to comply with this or that standard, but customs rarely inspect these. So you end up importing produce which is much cheaper than the local-grown one and which also doesn't comply with the strict local laws. That's where the "unfair competition" happens.
Sure, I bet French farmers aren't too happy to see tomatoes or whatever grown in other EU countries with cheaper labor flood the local market. However, anecdotally, I never see produce from eastern Europe here in Paris. Non-French usually means Spanish or Netherlands if it's EU, or northern Africa if not. You can mayyybe find son specialty cheese or meat from abroad, but outside the very common Italian varieties and Gouda, it's really not easy to find in regular supermarkets.
However, for some reason, apples from freaking Chile and South Africa seem very common, even in season, although apples grow fine here, including that specific variety (pink lady). And when I do find locally-grown ones, they're usually at the same price.
Edit: I've asked that myself multiple times. There's also some stubbornness there as well TBF.