Yup, hiking. Although we are going to be taking it easy. Doing it more to just get out into the wilderness and see the scenery than hump miles every day. Going to play it by ear, maybe bivouac a bit. Not sure exactly where yet, in my opinion the less populated the area is the better!
I'd have a look at the terrain type that you're going to be traveling in and tailor your 'survival' kit for that terrain.
I think your kit is well thought though for a lowland temperate environment. However the Pyrenees is not a lowland Temperate environment. Some parts are high alpine glaciated areas. Some parts are Alpine rock, Some are alpine medow, some are Montane forest...
Without sounding unduely critical. For example having a heap of firelighting kit is great but if there is nothing to burn in the environment you're in... Then it's redundant... My experience of Alpine above the 'tree line' environments is that wood is at a premium. Similarly 3 or 4 cutting tools are probably over kill.
I've spent quite a bit of time in the Pyrenees and it's a great environment sort of 1/2 way house between the UK hills and the Alps at full scale. There is some superb hiking. The mountains have some excellent scale generally it's a superb environment. On my forays and climbing I personally didn't feel the need for a kit as comprehensive as they one you have. But each to their own.
I think your FAK is good I'd add in some High factor sunscreen, some Immodium, and some hand clensing gel.
I'd personally ditch the majority of the fire lighting kit I'd add in some ESBIT tablets as they are sealed in a foil sachet unlike hexy these will do as fire lighters and also fuel away from a fuel supply. Add in an emergency high energy food source perhaps a couple of Leppin gel sachets or good old KMC.
I'd take a portable shelter that was small such as a bothy bag.
If you're used to UK mapping with the excellent OS mapping then French IGN maps are a bit of a shock. Based on this a small GPS like a cheap Etrex with the refugios and CAF huts pre programmed in in the area you're going to be might be well worth it.
HTH
John