Is the car an automatic transmission? Does it only do it in gear? Possibly the idle air circuit (IAC) is gummed up and not responding quick enough, so the car is stalling when you stop. By the time you take the car out of gear and engage the starter, the IAC has managed to open up the the start position. If it does it anytime you step on the brake you must have some weird electrical cross-talk that could be the devil to find. I would check the brake lights for a good ground (less then 1 ohm), then you need a good Peugeot mechanic.
When you hit the brakes the booster needs vacuum from the intake manifold. I wonder if this is causing the problem, whilst admitting that I can't think how it would kill the engine. Cheers
I know nothing about Peugeots but I did have this happen on an old Chevy V8. Seems the power brake booster had an enormous vacuum leak and when the valve was opened by pressing the brake pedal, the engine would lean out and die at idle.
