An EU government could try to convince your own government to enforce their fine / injunction / extradition / whatever. I don't think the USA has any treaty or other law that would compel them to. I'd guess that Trump's administration would treat the request as something between a joke and an attack on American sovereignty, so I doubt that's a major risk here. Other countries may vary.

The easiest path for the EU to enforce is probably through your customers and vendors, probably starting with payment processors--like, require everyone who processes payments in the EU to transact only with people who transact only with GDPR-compliant companies. My personal guess is that everyone with a business model that depends on breaking the GDPR will move offshore, and the EU will play the same game of merchant account whack-a-mole that the USA does for online poker and such. I'd guess that the effort to enforce offshore will be big enough that only the most egregious violators will be worth the attention.