Peugeot 107 Camshaft Sensor Failure

Those symptoms point towards a camshaft position sensor failure. The ECU uses that sensor to determine the camshaft position for proper ignition and fuel injection timing. When it fails, the timing goes off, hence the rough start and stalling. Have any engine misfire codes appeared? Also, check the wiring and connector to the sensor; a loose or corroded connection can cause similar issues.

Misfire codes did appear last week, but I cleared them. Wiring looks okay, but I haven't used a multimeter yet. What's the likelihood it's the encoder wheel on the camshaft itself and not just the sensor?

The misfire codes strengthen the camshaft sensor theory. A defective encoder wheel on the camshaft can cause the same symptoms. The sensor reads the wheel to get its position data. If the wheel is damaged or misaligned, the sensor gets garbage data. Given the mileage, it's not impossible. Without proper diagnostic equipment, you're shooting in the dark. I'd suggest taking it to a trusted workshop.

I dropped it off at the shop. It was indeed the camshaft sensor AND the encoder wheel was damaged. It cost 695€ to get it sorted, but it's running smoothly again!