Not GDPR-specific, but France.com had its web domain seized by France recently[1]. It was a private US-based business (not a squatter) that the government of France had actually cooperated with for years, until they suddenly decided it violated French trademark law and seized the domain. The domain itself had been in one person's possession since 1994.
Enforcement of national laws is very much a thing across borders, so private businesses outside the EU are right to be apprehensive about what is going to happen as GDPR enforcement ramps up.
When the first purely US based company is successfully fined or shut down by the EU I’ll believe in their ability to enforce GDPR.