10" long and it just stopped working stuck on same map position even after resetI doubt a firmware update would be the answer. Did the number of satellites that can be seen gradually reduce or was it a case of there one day and gone the next time you looked.
I'm not 100% sure of how the 308 system is set up but the parts that can fail are probably only the radio/head-end or the roof antenna/amplifier. That's assuming that the GPS antenna is combined with the roof antenna on your car. Is your whip a stubby affair or one about 10" long? Having said that, if the DAB is still working then there's every chance that the roof antenna is OK.
I suspect you may need to get the BSI read with a Diagbox to see if any errors are being recorded there. But I'm not even sure that that if the sat nav itself fails that it would throw up an error.
i have not tried battery yet I might give it a go at weekendUnless anyone else has any ideas I think your next step is to have the codes read. A Peugeot dealer will want something like £90 to do this so it might be easier just to ask them to investigate the problem as it stands.
Alternatively is there a Peugeot indie anywhere near you (where is that - you don't say) or maybe an enthusiast with a Diagbox near by? If you get the codes read by a cheapo code reader then this will probably not tell you anything that isn't obvious, you need a Diagbox or really high end (Snap-On, Bosch, etc) multi marque reader to investigate deep into the BSI and associated ECUs.
You say you have done a reset. Is this just of the radio or have you tried a BSI reset (switch off ignition, leave car alone for 5-10 minutes, disconnect battery, etc)?
Having said all of the previous I am still pessimistic that the radio head-end will need replacing.