How could Britain's acceptance of a French-backed emperor in Mexico serve British interests?
Short answerMaximilian could keep France and the United States occupied with each other, and that distraction could outlast the American Civil War.
NotesBritain's tolerance of French intervention can be understood as a calculation about competing powers. An emperor in Mexico could keep France and the United States occupied while discouraging other powers from intervening in the region. The American Civil War did not make that calculation irrelevant, because the war would eventually end. Maximilian's presence could remain a diplomatic problem for decades.