When our DD was about 22 months, we went to a campsite at Hourtin Plage (on a peninsula sort of , about level with Bordeaux), www.camping-cote-dargent.co.uk/. It is a short walk to the beach with small shops and restaurants, and they have a good pool area - outdoor pools with slides, and a toddler pool, and an indoor pool which is great, both to get out of the sun and if the outdoor pool is a bit cold (we were there in September). DD absolutely loved it there and we were able to take her on the big slides (one of me and DH posted at the bottom to grab her as the other one went underwater). She adored it and her water confidence went through the roof.
We stayed in one of the site's mobile homes, which was great. Only thing is it might be a bit big for you as it is a proper commercial site.
We stayed at Les Mathevies, and it is a nice site with an indoor playroom to get out of the sun which is good. The playground for toddlers is (or was, at least) a bit tired but it didn't bother DD and it is next to the bar area, so ideal if you fancy a drink in the sun while they potter.
The swimming pool is nice and there is a toddler pool, and once a week they organise a bonfire in the evening and the children toast marshmallows which is lovely (although your DS will need help obviously ).
As others have said nowhere is within walking distance, but Sarlat is a drive away and is a nice big town - while we were there there was a sort of sports thing going on in the town and loads of free activities for children to try including a sort of soft play gym thing.
Another place we enjoyed and which is (or used to be) a slightly smaller site than most Yelloh ones was Yelloh St Emilion. Looking now, it seems to have about 125 pitches and 47 rented accomodations.
There is a pool, a playground and a little lake and you seem to be able to hire pedal boats. St Emilion is a lovely town although, again, is a fair trek from the site. We used to do it on bikes but I am not sure if it is walkable.
We have done loads of holidays in France since DD was born and, so far at least, she has never been bored so long as there was a pool and a playground and possibly a bouncy castle about. We got a bit of time off too, as she napped and slept really well with all the swimming and running about.