Dear Joi
Goats might be shy, which is not the case for cows... who always look for company, especially in France.
Just Kidding. In fact goat cheese production can be everywhere (anywhere) from Vosges (North-East) to Landes (South West). You can always refer to a cheese map (not a gps) to locate production area, pick the name of the cheese which is linked to a Village or a small region, and roam around. Local tourist offices and cheese shop can be of help. The best is to look for local markets: you'll always find a goat cheese producer, where you can arrange farm visits if you buy some cheese.
This is an example
Map of France with Cheese-France
You'll see that goat cheese can be found for instance in Valencay (Loire Valley).
Just Google maps it, and you'll see it is between Vierzon, Chateauroux and Tours.
While doing an excursion to the Loire Chateaux, you might want to look around , you'll find hundred of local goat cheeses to taste and buy, in farms or town/village markets.
You might not be able to see the goat. And it might be good to ask....
I used to stay in Provence where goats are in diminution but you can still find here and there a good number of farms. Especially if you do not search in the immediate vicinity of coastal region, but in "arriere-pays" (our French outback sort of) they are plentiful. While I was in Corsica, goat cheese, coppa, bred, red wine and fresh grapes (maybe not in this order) were my daily lunch (picnic on the beach, or under a pine tree). One cheese per day. Mmmmmmmmmm. Take it easy with the wine.
good goat hunting.