It could be that the gear-change on this car is not as slick or tight as other cars you may have driven, and if the car has a high mileage, has had lots of previous owners/drivers, then it may not have been treated very well. 01 is not old, €5.2k is expensive enough and you do have a right to a car in serviceable condition because this is how it was described to you when you bought it.
The garage seems to hope you'll shut-up and go away. They have your money and probably don't want to be bothered any more.
Problem seems to be that you suspect there's a problem with the car and are apparently reliant on them to tell you whether or not there is - and they have no real interest anymore.
You don't make it clear what your local mechanic told you about the condition of the car. To be honest, it seems that he was a bit vague - telling you about tape isn't exactly a proper assessment and does not give you any leverage with the garage.
I suggest that you get hold of an automotive engineer (phonebook) or ask for a drivetrain inspection and report from a proper Peugeot main dealer. You'll have to pay for this but at least you'll have an independent assessment and a report identifying exactly what problems are from someone who knows.
If there is a problem, take it back to the original garage pronto and tell exactly what's wrong with the car, take no flak and tell then that you expect them to fix the problem at no cost. Try to find out if the garage is a member of one of the several societies for the motor trade and if they are, report them to the society immediately and ask about recovering the cost of the inspection you had done and any other expenses. You could also contact the office for consumer affairs.
It might also be possible to recover costs using the small-claims court process, which is free of solicitors, very cheap and quite simple to use.
If there is no problem, or if the issue arises because of acceptable wear and tear on an 01 car of that mileage, you'll be out of pocket for the inspection, but it will have been worth it to establish that the car you paid so much for is actually useable. I take it tho that you won't exactly be falling over yourself to recommend this garage to anyone!!