The colors of your wires are supposed to be the same all over Europe, but for sure are in Germany and BeNeLux.
Brown is Live, Blue is Neutral, Black is switched Live.
Your sensor switches 230 V AC to your floodlight "light projector".
You cannot use that to directly interface to your Arduino.
There are 2 PCB's visible in your pictures.
The second PCB, which is only visible in the 3rd. picture might have a relay (relais) on the invisible side.
You can probably alter the PCB so that that relay will not be connected to the 230 volts DC anymore.
Then you can use those contacts to switch your Arduino.
This still will require you to power the PIR sensor from 230 V, and i'm hesitating to advise you to do so (because you have to ask this question).
The pics also show there are 3 wires (in 1 flatcable) between the 2 PCB's.
It might be so that the second PCB works on 5 volts or can be changed to do so.
But to know this for sure, your webcam pics aren't clear enough to tell us anything more.