Normal to ask to transfer funds at hotel

Whether normal or not, just keep in mind that you have zero protections once you wire the money. Would Trip Advisor help you out if it goes awry? Once it's gone, it's gone (and then there is the issue of additional fees to wire the money). If it's a true mom and pop and they need a (small) downpayment (not the whole cost), that's one thing. But given how many choices there are out there with using a credit card to hold your place (with no prepayment), I would do the latter. Credit cards have much more protections built in than wiring money to someone.

I have never been asked to wire money for a hotel...proceed with caution.

I have wired money twice. Once to rent an apartment (didn't do that one - we worked out something else) and once to pay a travel agency in Egypt. I've never had a hotel ask me...what hotel is it?

The place we are looking at is Clos Saint Jacques in Marsault.

In many countries in Europe bank transfers between individuals or as a business transaction are nothing unusual - ones that typically historically had a giro-based banking system rather than a cheque-based one.

If you book that property through http://www.booking.com/hotel/fr/clos-saint-jacques.html, you can pay by credit card. Once you get there, it's noted as cash only.

I wired money to a bed and breakfast to reserve a room on the Isle of Skye in 2015.

As Laura points out, it's on booking.com, so you don't have to deal with a transfer, which doesn't exist in the States anyway and is different from wiring.

Fyi, bank transfers are so normal in Europe that Germans aren't even issued check books anymore. People can do it themselves at home transferring from their own accounts to an account number of another person or merchant, sort of like a direct deposit. Transfers take the place of checks and allow the merchants to avoid credit card fees. And as Agness pointed out, once it's deposited, it's gone, unlike with a credit card.

are you actually booking from a link from trip Advisor, if so be very wary,trip advisor has not got a very good reputation for their booking system or the parties they deal with ,numerous complaints on their support forums.
As other have said go through Booking.com, I have used them numerous times over the last 5 years or so without any issue.

Sarah use booking.com , we have used them for years safe and reliable .