Cyinder one fault

Run a compression test and a leak down test to make sure the problem is not a mechanical fault. If that tests okay, it is probably an injector. Swap #1 with #3 and see if the problem moves. If it does replace the injector.

Then run the compression and leak down tests and a fuel pressure test as well. What code(s) show up when scanned?

Okay, been looking at the fuel system and your symptoms. Get the fuel pressure checked and also run a volume test. I am suspicious that you have a clogged fuel filter or the pump is failing. Another remote possibility is that you have water or other contamination. That would have to go through the injection system and would cause many of the problems you are seeing.

If possible could you post the actual numbers for the codes. They might point to a fault or better idea of the problem.

Do you notice if this happens only when the fuel gets below a certain level? Only after it is parked for a while? Or is it all the time?

I just had a strange thought. When you replaced the coil packs/plugs, which end of the engine are you calling cylinder #1? I talked to a couple people in the UK who said that some of the Peugeots are "backwards" with cylinder #1 at the gearbox end (right side facing the engine) instead of the more common layout.

Okay, that negates that idea. In looking around this seems to be a very common issue that even the company has a problem with.
I would say to get the fuel pressure tested, and have a compression and leak down test done.

The only other item might be a short in the wiring harness to the injector or coil. Peugeot left the US market long ago so it is hard to find good information here.