"Butcher's Tale"

I'm nearly finished with reading Martin Gilbert's The Somme; lately, I've just been studying the maps in the back of the book.  Yester-day, I realized something about the places mentioned in "Butcher's Tale" - "And the flies came down in Gommecourt, Thiepval, / Mametz Wood, and French Verdun."

Coincidentally mirroring that "came down," the places are listed from north to south.  Here's a screen clipping I took of Google Maps:

I also started wondering why Verdun is specified as French when in fact all of these places are located in France.  As I understand it, both French and British Commonwealth troops were involved in the fighting around the Somme, but only French troops were involved in the fighting in Verdun.  The song seems to be from the perspective of a British soldier (in interviews, Chris White has mentioned his uncle who fought and died on the Somme), which somewhat explains this distinction.