There are currently no commercial services using Reims-Champagne airport.
Air Turquoise used to operate from Reims to four other French aiports, and to London Luton, but the airline went bust three years ago.
To get to that part of France by air the only valid routes (except for the Air France business flights from London City to Paris Orly) are via Paris CDG. See here for UK departure points:
http://www.frenchentree.com/france-flight-map/ #
Given that you'd have to take a train for the final leg of your journey (unless you hire a car) it might be better to use Eurostar. I've just checked some random dates in October and Eurostar are currently offering an inclusive return fare of �79 from St Pancras International to Reims. (Travelling from a different UK departure point often only adds a tenner or so, in each direction, on to Eurostar fares):
http://www.eurostar.com
Chris