BUT, it's much harder to US three-letter agencies to obtain access to data residing in France, or the other way around - that would require hacking, and that carries a much higher degree of difficulty and risk (not that I would ever imagine it doesn't still happen).
EU law does apply when national security concerns of non member states are engaged, though hence the Schrems cases succeeding (and why the UK in on shaky ground when it comes to equivalency decisions post-Brexit).
Eurpol is currently on trial for violating it, as was the German BND previously.
But it does have sister legislation - the Law Enforcement Directive[0] - that does apply many of the same principals.
[0] https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=celex%3A...