You're right when you say that, from 2006 to 2010, most of the cases at the Immigration Appeal Division were handled in English, even if it was sometimes a slim majority, for example from 49 to 51%. However, from 2006 to 2010, close to two-thirds of the cases handled by the Refugee Protection Division were heard in French.
It's important to understand that the procedures in each section are different. For example, let's take the Refugee Protection Division. It is very likely that, when the Canada Border Services Agency meets an individual who shows up at the border, the officer checks the "English" box or begins filling out the document we call the Port of Entry Notes. But the document that is used as a basis for proceedings here is the personal information form, which the subject must complete him or herself. It's on that form that the subject is asked to indicate which language he or she would prefer to use. The notes taken by the Canada Border Services Agency have no impact on the choice of language. This document, which we call the PIF, even in French, tells us which language the proceedings will be held in.