It's just called "the heaths" (les landes) in French, and heaths do support sheep. But I have indeed also heard the story of how it used to be a large marsh, so

It's just called "the heaths" (les landes) in French, and heaths do support sheep. But I have indeed also heard the story of how it used to be a large marsh, so I guess it was simply a patchwork of marshes and heaths. In any case, the area seems much too large to me to have been a single large swamp.