I had exactly the same problem and am posting this just to help anyone who suffers.
I replaced the Plugs, Coil Pack and Fuel Inlet Valve all to no avail.
As a last resort I changed the water temperature sensor at a cost of 12 pounds - that fixed the problem
Peugeot 206's use some form of algorithmic calculation based upon sensor readings. As it was getting inaccurate data it's response was just to shut down the engine!
Tom
June 2014