Easyjet offer flights from Gatwick to Bordeaux regularly in the summer months. These are available to book now. The drive from Bordeaux to Monflanquin is about 1h45min.
Flying into Bergerac Airport is another option, as Bergerac is slightly closer (40min to Monflanquin). Flights operate from London City airport (BA - released early September), and potentially from Stansted with Ryanair.
Driving from St Malo is another option if you don't mind a road trip (6h30m). DFDS sail from Jersey, with bookings open now.