Branner was drafted into the United States Army in 1945, serving in the later stages of the European theatre of World War II.

While a student, Branner worked in France at the École Nationale des Chartes and led excavations of the Bourges Cathedral between 1950 and 1952, the subject of his doctoral dissertation and an eventual book on the topic that won him the Alice Davis Hitchcock Award in 1963.

Throughout his career, he made important discoveries in the chronology and style of French cathedrals, incorporating cultural historical tools into the method of design analysis that had more traditionally dominated architectural history.

Branner also studied such artists as Jean de Chelles, buildings such as the Le Mans Cathedral and the Sainte-Chapelle, and manuscripts such as Fécamp Bible and the Psalter of Saint Louis.

[3] Late in life, he worked on the stylistic identification of different manuscript painting ateliers during the reign of Louis IX of France.