The LLM / foundation model industry will happily stay in the United States and ignore the stifling regulation of the EU if necessary. There is so much market share to capture domestically at the moment.
New laws would have to outlaw fair use, that will likely not happen as the only country that ignores such laws will win, especially now that the cat is out of the bag.
They can redefine fair use without removing it entirely. Thing like that happen all the time.
Will it be effective? Dunno, but LLMs aren't as easy to duplicate or execute as films are to pirate or watch, and yet copyright law still gets enforced somewhat.