It's a job for someone who knows what they are doing. A Peugeot mechanic I trust spent about half an hour bleeding the system on my Mi16 after a coolant replacement. Peugeot make a sort of "upside down plastic bottle" which screws onto the radiator cap and has a twist valve in the "top" to control flow of water/coolant into the radiator, it's pretty well vital to have one of these.
I wouldn't want to try to explain how to do the job, but my mechanic took the coolant temp up to 88 degrees (where the fan kicks in) three times as part of the process. He also spent time whacking the radiator with the palm of his hand, and also fiddled with the 3 bleed screws a fair bit. After doing this job he said to me "I'd hate to be trying to do this if I didn't know what I was doing." I believe him! Leave it to the experts.
The same guy strictly only uses the genuine Peugeot coolant. He told me that the heator cores are made of not much more than aluminium foil and in his experience the Peugeot coolant is the only stuff to use.
John