Cheap flights to Bergerac airport
With the explosion of flight routes and low cost airlines it is often difficult to keep track of which airlines fly which routes. The Skyscanner search (below) is probably the best way currently available to track the available airlines and prices.
For visiting the Dordogne region, Bergerac airport is the best placed possibility. When flights to Bergerac are unavailable Bordeaux or Toulouse are the best alternative airports. For the north-west Dordogne you might also consider Angouleme airport.