Auto security systems seem to do a lot of inexplicable things. Things we ordinary people would not expect intuitively. I discovered this last fall with my 2006 used Pontiac, as I caused the horn to blast simply by unlocking the door with the normal key. With some experimentation I found it happened if I flipped the door-locking switch before exiting the car. It stayed quiet if I had previously locked it with the same key. I don't know why the designers did this.
If you try any alterations whatsoever, you can't necessarily hope to reduce it to simpler operation as you wish. Instead, you may cause the alarm to activate and never turn off. Or the engine may never start again. The Peugeot dealer will no doubt offer to replace every module that has to do with theft prevention (at great expense to you). Probably he will simply restore your car to 'normal operation', that is, to do the same thing it does now that annoys you.
Look for manufacturer bulletins, or recall notices, which might address your situation. You can ask your dealer if you trust them to stay up to date. There is a slim chance the module needs to be re-programmed, at small expense.