First things first, check the car when idle (started but not running): is it overheating, if yes clearly something to do with Radiatior, Coolant, radiator fan and AC fan.
If car is overheating while move, then first thing to check in ur case as you touched the gearbox: Check the gear oil cooler next to radiator is working. Then get the gear oil and filter installation inspected with trustworthy mechanic.
If you have jerky gear transmission, check the oil you used is same spec as Peugeot recommends or different. Never use diff oil, better get oil and filter from Peugeot dealer and replace.