It really is a piece of string question because one “probably one storey” extension can be very different kettle of fish from the next one-storey extension, and especially if BdF is going to specify the building style and materials to be used. What other people have paid for their extension could turn out to be streets away from what you would pay for yours. As David says, the only person who can give you a valid answer is an architect, who may be able to anticipate what conditions if any will be laid down by BdF.
If the building of the extension is a make or break factor in the purchase, I would suggest that you establish whether you would even get permission, before you go ahead, permission is not automatic.
I also found BdF very helpful - all I was doing was a ravalement de façade but a chap from BdF rang me up to make sure that I understood what materials to use and wasn’t planning to apply modern products to a 16th century building, that wouldn’t let the fabric “breathe”.