This recipe pretty much uses champagne like any other wine to deglaze the pan after you've cooked the pork chops. Then you thicken the sauce with some flour mixed into some milk. The sauce does not have a strong champagne flavor, but the sparkling wine did add a sweetness to the sauce that complimented the shallots and worked well with the thyme.
As a side note, I got to use my new potato ricer to make the mashed potato side for this dish. Normally I just use my masher to make lumpy mashed potatoes. But this new ricer extrudes the potato through small holes, kind of like a Play Doh factory. The end result is a much smoother mashed potato. What a delicious way to kick off 2010.