I would tend to agree that Ariege is one of the least populated and most unspoiled regions of France, which is most likely the appeal for you. However imho there are some fabulous, unspoilt areas (with a more favourable climate) in departments not too far away from there. I'm in one, and relatively Brit-free thank goodness - but I ain't saying no more.....
Good luck with your house hunting.

Look on leboncoin.fr to buy a house, that way you can avoid paying extortionate and inflated estate agency fees. First bid, I'd knock 30% off.
After living in the Toulouse area for 11 years I can't count the number of times a french person asked me if I knew any English people looking to buy a house. Why? Because "we" will pay more and bargain less than the french ones.
You can get the buyer to ask the local Notaire for a valuation - these tend to be more realistic than the prices the agencies are asking since the notaire's office will know how much the houses actually sold for.

Houses take ages to sell in France, the average is about 1 year and if you're moving abroad afterwards be aware of the taxes/time limits that may be charged when you sell the house.

If you want wi-fi at home I think you are probably going to have to pay a full-time contract (there was a thread about this recently on here)

30% off would be very appealing. I had sort of noticed the vast price discrepancies between French property sites and English ones and was working on the basis I would probably be stuck with it until the Chinese take over the world. Hence I want to stay cheap. The taxes whilst trying to sell are good advice. I am working on paying 7% purchase price in notaries and agency fees and then 20% of perceived rental income per year.

I thought purchase fees worked out at around eight point something.
The buyer shouldn't have to pay immo fees unless you pay someone to househunt for you and hold your hand.
You can't second guess the property taxes and it is dangerous to assume, you need to actually see the figures for that particular property. 20% is not a bad average benchmark but for some properties it's way higher and for others it's way lower. A lot of different factors come in to the calculation, there is always a reason for why they are what they are but it's not always obvious especially for an incomer, as local politics have a bearing as well.

The French are neurotic about square metres.
They normally ask what the sq.m. is for each room; garden; terrace etc.
An estate agent would expect you to ask this frequently.
On this basis, it is a good idea to compare properties on the price per sq.m.
They can vary a lot depending on location and condition but it gives you a good comparison when looking at various properties.

if you want to know how much the frais de notaire wil be then you can use this calculator.
Frais de notaire : Calcul de vos frais de notaire | De Particulier à Particulier - PAP

I know that the buyer isn't supposed to pay the cost of the agent selling the property but that amount will be included in the price of the house. I know because I sold a house in France last year....we sold on Leboncoin for a little over the amount that the notaire's office said our house was worth.

If you do go to look at a house then the owner/seller's agent will expect you to ask about the taxe d'habitation and the taxe fonciere and so they should have this year's bill to hand. Also ask about electricity and gas bills, again should be to hand for you to see the actual bills. If they're not, well, that's a red flag.