I agree with other comments and would be patting myself on the back to achieve the number of bookings you have, but in the interests of always trying to do even better, I'm going to nit pick.
I agree with LV that travel directions from UK definitely need to be there with more prominence that the US international flight info. I think you're 100% correct to think HL is not used by US people very much, if at all, even so, I would like to know how far from London, Rome, Brussels, and other major European capitals that might be included an American taking a multi country EU tour. Just a thought.
Also, I'm going to make a couple of general comments not relevant or specific to this listing. I hope these aren't too harsh.
The house is perfect for a romantic getaway for two, for a small family taking a break from their busy routine, and for two couples traveling together.
Never say anything like this. You are immediately excluding everyone who doesn't fit into your idea of what a renter looks like and it's really not your place to tell people if it suits them or not. You can emphasize certain features - romantic setting, but that doesn't have to be two people, frankly it might be a jolly threesome, and lots of people travel together who are not couples. half your audience is thinking whether or not they fit into what you're describing.
Second generalization - your first paragraph is all about the house - not the lifestyle experience you can have in it - yes, I know, that's what the listing sites ask for that in that first paragraph, with activities further down, but it's a flaw in the system in my opinion.
It's good to put them into the location by giving them a taste of the experience somewhere in the first three sentences in my opnion. This can be done by turning a sentence around. For example, instead of saying, "Our two-bedroom, three-bathroom house is situated directly on the banks of the Armançon river, with spectacular views of the medieval town ramparts through the weeping willow trees that gracefully drape their boughs over the river's calm water."
Instead you could say, "Relax in the gardens on the banks of the Armancon with spectacular views etc...., then go on to say there are 2 beds, 3 baths. I don't have exact words, but the idea is that they imagine themselves there late evening before bed - views first, then bed. Or if you want to do it the other way round, then you have to talk about waking up in the morning in 2 beds, 3 bath house, and taking breakfast on the banks of the river.....
Not sure I'm explaining myself clearly, not least because these are quite subtle tweaks to what is already good and I'm in a bit of a rush, anyway, hope this helps. Otherwise, feel free to trash....
Otherwise it reads very well!