I would argue that this is a bad definition because what you described is just operating in a jurisdiction but without localization.
I prefer the definition where you're making money(directly or indirectly) by providing services in a jurisdiction.
An example would be collecting French users data and then selling it to ad agencies(or being acquired by Google?).
Accepting payments in USD is a pretty clear signal that a website mostly cares about US users, and if someone else uses the website, oh well, it happened, doesn't really change anything under GDPR.
(although you probably could have French support anyway, just expand the website to Canada as well ;), of course it isn't the same French as in France, but it's still French somewhat, EU currencies are trickier however)
- Or in case where you aren't located in EU, providing services specifically to EU residents, which can be hinted by having a language choice mostly spoken in EU countries, allowing EU currencies (Euro, British pound and so on) or specifically mentioning supporting EU, for instance by saying that your website can deliver packages to European Union.
Facebook for instance has offices in EU, which makes it clear that they are under GDPR, but even if they didn't, they do provide Facebook in EU languages.