You might consider the Dolomites north to south. there are quite a few options and the walking is through staggeringly beautiful scenery, (both literally and figuratively) and you can add in as many diffcult bits of via ferrata as you wish en route. The huts are generally excellent and there are plenty of small towns en route in which to re-stock and refresh.
You didn't say which month but if you,ve a choice I'd leave it till after August or before July. Being that bit further douth it gets scorching in the valleys.
A lot depends on your level of fitness but if you left the car in the vicinity of Glenmore Lodge, or higher, made your way across to the Lairig via the Chalamain Gap then headed through the Lairig to, say, Derry Lodge for your night stop then returning the next day via Glen Derry and the track to Nethy Bothy thence back to Glenmore you'd have done one of the greatest walks in Europe. At this time of year you'd want to start as early as poss. as the nights are racing in but as this is all low level (in Cairngorm terms!) you can push on. Good paths all the way except for bits of the Lairig and if needed, an escape at the Derry Lodge end.
Paul, if this is a medical problem and not just unfit feet, you can get made to measure insoles on the National Health. I tried all the usual options before being pointed in that direction. We have a couple of podiatry clinics,(maybe 3), here in Edinburgh and they give a wonderful service, that is, once you've found them. Tests, made to measure and allowed a new pair every year, you soon have enough for all your footwear. You may have to go through your GP, at least first time and don't be put off by the dozens of old codgers waiting to have their corns done. When I went to collect mine the first time I could barely walk from the car to the clinic - next day I was back in the hills.
Yes there is a super Decathlon in Nice. I've mislaid my Nice street map but from memory head West along the Promenade des Anglais, that's in the direction of the airport, until you come to a major junction with the road going North to Grasse,(I think). Take that road North for less than a mile and lookout for a large shopping centre to the right. There's a Decathlon and its sister store in there. Great store. Excellent walking poles for less than £20./pair. Huge camping centre; they will certainly have what you want.
I'd agree with Steve. The Tourmalet is the place to see the tour but you might have to arrive a week ahead to find a place to watch! Gavarnie is more than a little busy; it's absolutely mobbed by coaches up from Lourdes. Mountainous pilgrims being loaded on little donkeys to be taken up the dung trail to see the Cirque. BUT! Late afternoon and they all vanish, leaving a quiet, rather pleasant little mountain village. I've never seen such a transformation. Gavarnie has decent hotels and great walking.