None of this is to say that the US system is better; it is better in some ways and worse in others (notably sentencing).
A nation of laws doesn't exist when the judges discretion in favor of the Police who 'are trusted' and receive deferential accommodation over the rights of civilians to expect the laws/rules enforced on the government even if inconvenient.
The French system can be completely different, but, if you follow the logic of the law, it's matches what happens in practice, it's a valid legal system. The USA does not have that, because while it pretends warrant are required in actuality they aren't and requirements/protections for citizens can be waived away by judges under 'good faith'.
So many times people rail against a wealthy person who gets off lightly from some offense because their representatives have successfully argued that a punishment would be unduly harsh, or that there were particular mitigating circumstances. I usually disagree with people demanding a tougher punishment, but that is a similar principle at play. Personally I would rather have all persons charged to receive dispensation for circumstances rather than only a few elites. Similarly given the choice I'd want protections against illegal search and seizure to be for all, but when you have no power to make that happen, what is the best second option? A privileged subset, or everyone universally worse off?
Search Lexus/Nexus for 'chain of custody' and 'good faith'. If the judge can waive away supposed rules/requirements/process violations with the blanket 'good faith' (that the court just blanket trusts that police were acting in good faith and not attribute maliciousness to their failure to comply) you don't actually have a system of rules/justice, you just have window dressing to make it appear you have a system of rules and justice.