Not sure it will be the fault of the garage as they would not have touched the gearbox during the service but I would get them to confirm this by you calling them and explaining the post service faults and see what they say.
They won't want to touch the auto transmission as it is beyond most garages - try Googling for auto specialists in your area who should be able to get closer to a diagnosis. To me the transmission is crying out for a fluid change.

 

HI,
Do you mean the change of gear oil?

Ken

 

A service is a service regardless of what make of car its not rocket science its possible they have drained transmission oil and not replenished it with correct fluid but gearboxes are generally not touched in a service.

Is the engine sounding ok a bad running engine will affect an auto box badly

 

You are correct. They drained some gear oil to change then they realized they dont have the right gear oil for my car. They ask me to contact them after few days to change the gear oil when they have it in stock. Engine is sounding good.

 

How about the car ? is it cured yet ?

 

What is best type of transmission oil for peugeot 408 2012 model and the recommend capacity of the gearbox (how many liters)