I don't know a lot about furniture, but I'll bet there are good reproductions out there. Not sure if the beautiful chairs Bush and Cheney are using are James Monroe-era or what they're called, but this photo is captioned with "Chippendale style Gainsborough Armchair
The webpage calls these Hepplewhite style
I am attracted to this style, too, but have no idea if it is French or English in origin or what to call it or anything. I just know I like it!