Its an often said that during most of the war the Trenches and fortifications of the Western front ran from the Channel to the Swiss border. However the vast majority of action occurred in the Northern parts of the front, the Somme, Flanders etc and nothing much further South than Verdun which is only about halfway between the Channel and Swiss border. I was wondering why this was the case as I can't find a satisfying justification, particularly towards the end of the war, when the arrival of American troops would surely have allowed the allies the numbers for wider allied action.
There were engagements, they were just limited in scope by the adverse terrain of the region. Most notable was the Battle of Hartmannswillerkopf, where the trenches ran up and down a mountain and fighting over the 1000m peak was fierce.
The reason more battles happened in the North was simple geography. It’s much easier to fight a war across the plains and rolling hills of Flanders and Northern France than the Vosges Mountains. The most Southern Battle of the War that you mentioned, Verdun, was itself fought on rocky, mountainous terrain that would’ve otherwise been avoided if it wasn’t for the German propaganda value of capturing the historic city.