The Tour du Mont Blance I think is just over 100 miles, the Cotswold Way may be similar. If thats your kind of limit perhaps hike half the Pennine Way from Edale, or half the Coast to Coast perhaps. I dont remember having drinking water problems on any of these routes. Sorry, tell a lie, the section from Byness to Kirk Yetholme can be a bit awkward if the weather is hot and sunny, no water at all in between if I remember correctly? As an alterenative to your car, you could of course consider a coach from Victoria Station to Chamonix, swapping at Paris. Thats what I did, took a while but it was easy and cheap, about £40 when I did it. I did find the site
www.rometorio.com very useful for planning routes. The company that I went with is part of the DFDS railways company in France. The coach was so luxurious and included free wi-fi. And of course going by train is very good as well. Both train and Coaches stop in the centre of Chamonix.
Back to water. I use a 2L bladder which sits in my rucksack and I drink from a tube slung over my shoulder. I only carry one small bottle as my emergency supply. I also carry a Lifestraw filter, this was cheap at the time of purchase, its just a plastic tube about 7" long, so easy to pack and I find it perfectly adequate for my needs. When I'm on the trail and don't want to keep sipping from my water bladder I find that cattle troughs are a good scource of water. I have a small plastic cup hanging from my rucksack and I just put it under the ball valve and collect, I do not take the water from the trough itself. If I'm a bit concerned about the water quality I just stick my Lifestraw in the cup and then suck and drink!