I can understand you must feel let down by your car & Peugeot.
Have you tried using a different device? Just a thought, it could be the device you are using, rather than the car.
If it proves to be the car after trying a different Bluetooth device, I would definitely have the car back to the dealership & ask them to sort it out. If there is a warranty, then they might have to replace the unit.
If there is no warranty, you might be better taking it to a specialist car audio centre. They would probably be cheaper and do a better job, but it will probably involve changing the unit in the car, these things are hardly ever repaired nowadays, just replaced.