Neighbors called the police because I was a bit noisy, they talked to me and made a photo of my ID. Who will have access to the info that police intervened and will it influence the decision on prolongation of my titre in France? How to know if I was "verbalized" or not?
Most of the time in France, when police comes because you are too noisy, they will begin by asking you to stop and it will end here if you comply (and don't start again once they are gone).
I forgot to mention that it depends on what kind of noise is involved. If we are speaking either of partying/music/tv or home improvement noises, the above paragraph will apply.
If we are speaking of loud dispute or someone shouting for help, things will probably be different as police might want to investigate what's going on and prevent potential crimes
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They might nevertheless fine you if they feel like it (see https://www.service-public.fr/particuliers/vosdroits/F612). They could either give you the fine receipt on the spot or send it by mail a few days later. That is not very common.
As for the picture they took of your ID, that is really uncommon and I am not even sure that it is legal. That might mean they wanted to check your ID once back at the police station, but this is usually done via radio communication.
I would think that there will be no consequences, unless you were facing over-zealous police that wrote down this on some unofficial register because you are not a french citizen.
(Source : experience as a native French citizen)
If you'd been written up, you'd have been given a paper on the spot, most probably. Or in the mail, soon after the incident. Since you didn't get anything, you still have a clean record, I believe. Besides, a noise infraction isn't criminal, so it wouldn't influence the renewal of your resident permit. Heck, these days, even foreign convicted criminals are hard to expel...
As for the photo of your ID, it could be they were too lazy to write your details down, to check them later at the station. So they took a pic, instead of writing. Again, if you haven't heard back from the cops, you're in the clear. Just keep the noise down...