I think you need to be slightly more picky with a location. France is a huge country with every kind of geography. Do you want to be near mountains, sea, forest, lake? Near to the UK or another country?
Renting an unfurnished house involves signing a 3 year lease. (You can get out of the lease with sufficient notice, as long as you follow the procedure.) And you'll find that most rentals in France allow dogs with little problem.
As for the rest of it, you really need to make an exploratory run to see the available properties for yourself. Pictures lie (especially pictures on the Internet) and most landlords or rental agents want to meet potential tenants face to face.
You also have the issue of your credit worthiness to deal with. There is no credit history or credit record here in France, so most landlords want to see three months' worth of payslips (from a French employer) and/or three months' worth of bank statements (definitely a French account that they can tap directly for the rent).