Just in case this helps others -
Stop start hasn't worked for a while on my just over 4 year old DS4, I suspected the battery. Took a bravery pill and a new AGM 096 battery and did the following.
Turned everything off, auto lights etc inc. Wound down drivers window and shut door and also opened bonnet. Went for a cuppa to give the car time to shut everything down.
Took off air cleaner cover and fuse box cover. Removed cover on top of battery to reveal lots of wire connectors with fuses. Fiddled around and found two (three?) clips that released them. Unclipped main power lead from battery. Undid 10 mm nut that realesed cable from fuse cable array that allowed it to be moved to the right a bit (as you look at it).Then pulled the plastic cover over the battery forward and up (sharp tug required) and it will slide out forwards. Now its a long extension and 10mm socket and undo the bolt at the bottom of the battery left side as you look at it to release the battery. Then undo the post clamp with the same socket and extension at the back of the battery and lift off the terminal (bit of a fiddle). Now pull the battery forward and up and its out!
Put the battery back in in reverse but leave connecting power until the last thing.
Then its BSI reset procedure.
10 seconds later turn on sidelights
(or headlights) without opening the door a few seconds later turn on ignition by reaching through the open window.
Then the internet info varies.
I then started my car. All worked perfectly.
Some sources say turn off ignition and then back on and start, no idea which is correct.
Reset clock time and date and thats it.
I don't see my DS4 being that different to others but it is a fairly intimidating procedure for a first timer so make your own choice about getting it done for you or not.
After a short drive my stop start now works every time whereas it wasn't working at all before. I am sure the battery would have gone on for some time in normal use but these newish AGM batteries do seem to have a shorter life and cost alot more than the older lead acid type of batteries.
Good luck with yours
My DS4 is a 180bhp EAT6 2015 model