My wife and I and our 4 cats live in a large house in the Gironde (33), with 1 acre of garden/fields, and surrounded by vines. Attached to our house, but having its own independent access, is a comfortable, centrally-heated roomy 2-bedroomed gite which we use for friends, family, etc., but which we do not rent out commercially on a regular basis, although we might do so occasionally given a suitable situation. The gite is fully-furnished, with a huge lounge and a large,l fully-equipped kitchen/diner.We are in beautiful countryside about 5km from the nearest town (Ste-Foy-La-Grande) and 2km from a small village (Les Leves et Thoumyragues) with a bakery, post office, petrol station, restaurant, etc. Having a car here is essential. We are in a very small hamlet of 4 houses, two of which are currently unoccupied and for sale, and one of which has a charming French family in residence for part of the time.
Dealing with your essential requirements:
Our garden is partially fenced, but we do have two cat-secure enclosures (completely fenced and net-roofed), with lockable gates and cat-flap entries. One could be made available for your use. The gite does not have its own private garden, but you would be welcome to share the use of ours. The Gite does have its own patio and a parking space.
Very cat friendly!
As to your budget, are you referring to a monthly or weekly amount? (You have not specified this). If monthly, then this would not be adequate. We would seriously consider a 6 to 12 month let.
By local standards we do have a strong and mainly stable internet connection, which does cover the gite.
As explained above, we are quite rural but close to all amenities and, whilst not totally isolated, we are not crawling with neighbours. There is, however, a large pool of anglophones within a reasonable radius.
As to your options:
The gite has a shower room with thermostatically-controlled shower, vanity basin and toilet. There is no bath-tub, but our own house has a ground floor bathroom with a bathtub which could be made available to you. The gite also has a second toilet.
We have a heated indoor swimming pool (with shower room and toilet) of which you could have shared use. The pool is sanitised by an ionisation/oxidisation/subsonic system, which avoids the need for chlorine or salt. The only chemicals used are for regulating the pH.
Eco-friendliness is a big and broad subject. We support ecological friendliness, but perforce drive petrol and diesel vehicles, have oil-fired central-heating, etc. We cannot afford to buy new, supposedly more eco-friendly vehicles, nor change our heating boiler. The gite has double-glazed windows and we have recently replaced the former roof with a new insulated roof. Organic foods can be purchased from local growers, livestock-raisers, a bio and health food store at Ste Foy, and from market stalls every Saturday at Ste Foy.
I hope the above has given you a flavour of what we can offer, and if it interests you please feel free to email me at: firstname.lastname@example.org or by telephone on: 0557460315.