This area is difficult to label, as battles raged across a wide landscape, spanning regions, which is why you often see Champagne-Marne, Aisne-Marne, Oise-Aisne, etc.
It was home to several battles throughout the Great War, such as the First/Second/Third Battle of the Marne, The First/Second/Third Battle of the Aisne, and more localized battles like the Battle of Chateau-Thierry, and the Battle of Belleau Wood.
From an American standpoint, the most common name is the Champagne-Marne Offensive. This was the last major German offensive of the Great War, and was blunted in a few days, due in large part to the AEF’s defense at the Marne River.
The second phase of the battle in the area was an allied offensive, commonly known as the Aisne-Marne Offensive, which contained the Second Battle of the Marne and the Battle of Soissons.