The Via Michelin routefinder is by far the best website for planning your journey:
http://www.viamichelin.co.uk/
'Western France' encompasses a vast area but, for example, the journey from Eurotunnel to Bordeaux is quoted as taking just under 8 hours (plus, of course,the breaks which you'd need to add on), covering about 540 miles (nearly all on motorways). Toll charges are around £45.
The reason my mind turns to Bordeaux is that I was there a couple of days ago. It's a stunning city, with a vast area classed as a UNESCO World Heritage Site. It exudes 'class' (with loads of fashion shops, quality chocolatiers and, of course, wine shops everywhere). Prices are reasonable though, with a good three-course lunch, in one of dozens of smart restaurants, costing between €12 and €15 (including the all-important 'vin compris'!).
Draught beer, in a back street bar, is around £5 per pint.
The Bordeaux area would be a good base for touring. It's close to the coast but with loads of inland attractions as well. The weather in that area is 'warm to hot' for most of the summer. Although the proximity to the Atlantic coast means that rainfall is relatively high, it's unlikely to be a major problem for most people. (It's been dry and warm every day this week, except for Wednesday - when I was there! But, even with light drizzle all day, it was still warm and plenty of people were sitting outside the cafés).
Chris