A low battery can cause failure to start as the electronics require at least 10 volts to work properly.
The car may have entered "economy mode" if for example, you were cleaning it with the doors open and radio on and run the battery down to trigger the warning. Normally this isn't a problem and the car starts normally, but apparently Peugeots can occasionally be a pig to get back out of this mode.
One trick is to run a thick wire from the battery positive terminal directly to the starter motor and force the car to turn over with the ignition turned on. This makes the car start and come out of Economy Mode. Once started leave the car running for half hour or so to let the battery charge up and for everything to reset itself.
After a flat battery you can get indications of full communications to all units and no fault codes - just no start. Martin Robin Swinden shows a way out of this lockout using PP2000.
Martin says - The only way I have overcome it is to run PP2000; and enter into "new vehicle preparation" menu. It asks all sorts of questions you can't answer but by lies and intuition noting down the answers, getting rejected then trying the other options you will finally get to the bit where it says "Program whole vehicle" - you will need the pass card with the car immobiliser code. Enter and by a miracle not more than 30 secs later it should say "turn key to start" - and it does.
The first time Martin did this was after sending his ECU and BSI units to test centres to be checked over. Still no start. With nothing to lose Martin went for it with PP2000, and was successful. He reckons the security chain to be KEY - BSI - ECU and the loss of continuity seems to be between the BSI and the Engine ECU which have stopped talking to each other (plus the brake light switch on autos).