Abbreviated History Lesson
The Cathar Trail certainly exists and, from what I've seen, it's a scenic, easy walk without much long stretches of abrupt elevation change.
But it has nothing to do with the Cathars. The notion of the Cathar Country (Pays Cathare) was something invented by the Aude tourist bureau sometime back in the late eighties. The movement actually (and arguably) started in either Bulgaria or Germany. The largest concentrations were in southern France and northern Italy. Total adherents only numbered in the few thousands, including those in England.
The initial, early castles in Languedoc were built by both sides along the shifting Aragon/France border during the Aragonese/French Wars and thus pre-date the Cathars.
The Cathars actually lived in lightly fortified familial homesteads of less than a hundred people. In comparison, thousands of workers were required to build the Edwardian castles and thousands more were employed in the supporting structure to provide food and such.
The later castles were post-Cathar.
The only real link between the Cathars and the castles that comes to mind is during the Albigensian Crusade when a couple hundred Cathars had holed up in what was left of the castle at Beziers and subsequently massacred by the Papal Legate.