Check "conflict of laws" and "conflict of jurisdiction". I don't know the US legal system well enough to find it, but it happens in European countries (e.g. french judge applying US laws), so I guess it would be similar.
Moreover a US judge might not care, but a French or German judge might decide he is competent (if there are good reasons to think the website is not US only).
If a french or german court decides that a foreign company is violating their laws, they can do little besides preventing them from reaching their market, which would in this case mean that they can order ISPs to block the site. I'm pretty sure that there is no way that they can actually make a foreign-based company abide by their laws. How would they enforce the ruling?
Of course, if the company in question also owns a EU-based daughter company through which it operates on EU market (as Facebook apparently does), then that's a whole different ballgame.
Moreover a US judge might not care, but a French or German judge might decide he is competent (if there are good reasons to think the website is not US only).