For no reason anyone seems to know, the BSI forgets a key occasionally, and it has to be "reminded". (Quite probably, your battery disconnection was the cause) This requires the use of Peugeot Planet software and the proprietary interface between PC and car known as a Lexia or more correctly Proxia.
Now, you can buy this on EBay. The interface is usually accompanied by a CDROM with the software, which has been suitably modified for private use (to put it politely). Installation is not easy, but there are tutorials on YouTube. Use of the software to program the key is less difficult, but the precise actions depend on which version of the software you have. If you read around the subject, you will find that you cannot program with a previously programmed key, because an area of memory in the key is write-once, but the exception is if the key is being reprogrammed to the same car - the process will attempt to write the same code into the key, so it does not matter that that stage does not work.
On the Peugeot Forums, there is a map maintained of private people with the kit, who will do the job for you for an amicably negotiated fee much lower than a professional.
link.
Alternatively, ring around for a pro. Specify that you don't need a new key because it's the same car, and enquire the price.
One key will not start the car. It previously worked fine. All key internals are present and correct and fob battery fine. I have tried to program it using the instructions in the hand book, and variation on here, but no joy. Car will turn over but I think immobiliser kicks in. No faults shown on display. After BSI re-set the other key is still working fine but no joy with this one.