You need to sync the BCI with the 'Active fuse box' under the bonnet - can't remember the name of it!
Usually, this can be done by leaving the ignition switched on for ~30 mins with a BSU connected, following the procedure below will help

PROCEDURE FOR BATTERY DISCONNECTION

Whenever a vehicle battery has to be disconnected, switch off all equipment, interior lights etc,
close the doors leaving the drivers window open.
Switch off the ignition and remove the key and any diagnostic equipment.
Wait a full 3 minutes before disconnecting the battery.
The BSi must be allowed to go to SLEEP i.e. into "active economy mode". Do not operate any
equipment on the vehicle during this time. Remember, even opening the bonnet
will wake the BSi on a vehicle fitted with alarm.
If the battery is under the bonnet, open the bonnet first and leave it up.
ALWAYS disconnect any diagnostic equipment and do not operate any other vehicles during the 3
minute waiting period.

PROCEDURE FOR BATTERY RECONNECTION
Unless otherwise instructed by Peugeot or Product Service, you must always carry out the
following procedure, often referred to as a "soft re-boot", to minimize the
possibility of the BSi corrupting its own software when reconnecting the vehicles battery supply.
Ensure the procedure for battery disconnection has been adhered to and importantly all BSi
functions were switched off with the drivers window left down.
1 Close all doors
2 Remove ignition key if left in ignition
3 Reconnect battery. DO NOT open any doors
4 Wait 10 seconds
5 Switch on headlights through the driver’s window
6 Switch on ignition then start the vehicle and check system functions

Yes, very familiar with that procedure. I could do it from memory when I had the 406. It went through a spate of getting weird faults needing a bsi reboot to sort.
Eventually bought a copy of lexia and cleared all faults using it and the problems stopped.