One of the reasons that the Nazis were especially effective at finding Jews in the Netherlands is because of their very detailed civil registry, that included religious affiliation.
French authorities were also forced to help the Nazis locate Jews during their occupation, and this is one of the reasons the French today don't keep official records on people's race or religious affiliations.
Just because you fully trust authorities today doesn't mean the guard won't turn over in the future for any number of reasons.
At the point where you've already been taken over by the new "Nazis" it doesn't much matter. They'll put into place the systems you fear anyway. You say the French today don't keep official records on people's race or religious affiliations, but corporations do, and so that data on the population already exists and could be obtained very quickly. The nice French government today won't touch that data, but New Hitler would.
In the meantime, because France doesn't want to consider race in statistics, it's made documenting, understanding, and addressing the massive racial discrimination problems they have very difficult. For years there have been calls for the French government to start collecting ethnicity data in their statistics because blinding yourself to problems means you can't solve them. (https://repository.uclawsf.edu/hastings_international_compar...) The policy to avoid that kind of data collection was well-meaning, but it turns out that not collecting that data doesn't adequately protect the people of France, and in fact it's actually hurting them.
Very few people would be happy with their lives if there were suddenly no surveillance at all. There would be crime, corruption, disease, pollution, extinction, and abuses of authority everywhere. We'd be totally blindsided by extreme weather, incoming asteroids, solar flares, and earthquakes!
One of my favorite forms of surveillance is body cameras on police officers. Body cams are amazing tools! They help protect the police from false claims of abuse and aid them in training, while at the same time they help protect the public by helping us find tyrants and corrupt cops.
These body cam systems aren't perfect (tapes "go missing", some cops can turn them off) but they can be improved, and they should be because surveillance (like most valuable tools) isn't all good or all bad. Don't throw away powerful tools because you fear how they can be abused. Develop systems of transparency, accountability, and (ironically) surveillance to make those tools work for our benefit.
Also, just stop there!,
because the rest of that sentence will change every 5, 10, 50 years, no matter what anyone does.
Don't start any program within your home that you don't want your enemies to have access to use against you while they're in power.