Looking for green rolling wooded countryside in southern France

Hi, what you are asking is impossible to respond to. There are so many options. I suggest you do the work yourself, get in a car and drive around, nobody can chose for you, we all have different tastes.... have fun!

Yes, I agree with the above comment..
If 'verdant' countryside is at the top of your wish  list, then perhaps the Pyrénées-Atlantiques would be a good place to start - even though it's outside your area of interest. There's a reason why it's green though!
I admit that I'm biased - we've been in Bayonne for 11 years and yes, it's an "all year round" town, we can find wooded walks within easy reach and there's no shortage of cafés. And being set back 5km from the coast, It's not a beach resort. In the end though, as Tevisbuckles said, only you can make your mind up. 
One of the great pleasures of 'finding your niche' in France is the exploring and trying element - and not forgetting that all-important 'out of season' visit. Once you narrow your search area down, then maybe you could try  a short term rental to see how an extended stay goes. Good luck..

I’ve been happy in the area of Saumur, which is as you describe, and is on La Loire.

Thanks for that sensible reply, I am more than aware the size of the area that's why I'm trying to narrow it down and perhaps even 'discover' some not so well known towns. I have plans to rent out first but need to target the right area.

Thanks