GJC, Vatican I is talking about the extent of the pope's powers. This is not applicable to our situation because no one is questioning that the pope has supreme jurisdictional or moral power. The question is - what, if anything, changes to the pope's powers if he appears to lose the faith? This V1 quote does not answer that question.
Our situation is distinguished by 2 important factors - 1) the issue of heresy and ipso facto excommunication and 2) what penalties does ipso facto excommunication actually enforce (in the case of a pope). Sedes say that if one is ipso facto excommunicated, they lose their spiritual office immediately. I would agree with that and I think Fr Chazal would too.
Sedes also further argue that heretics also lose their MATERIAL, governing office/jurisdiction immediately. In the case of a pope, I do not agree, nor does Fr Chazal. Theologians are split on this question when it comes to the papacy. In the case of a bishop, the answer is to wait for the Church to act through canon law, a court decision, etc. This is easy and straightforward. But in the case of a pope, canon law does NOT give legal outlines on how to handle. Many theologians have argued that cardinals could call a council and depose a pope. I would agree with this; makes sense to me. Outside of this, there's no other concrete answer. All else is theological opinion, which carries no weight or legal precedent.
So Fr Chazal's view, that a heretic pope who is ipso facto excommunicated still retains his MATERIAL office, follows canon law. This view follows reality, since in reality, the pope and the many cardinals/bishops/priests who are the church hierachy do hold their offices, but are spiritually impotent because they have given up the faith.