The Pope can hold a personal opinion that is in error, but so long as it is on a matter that does not touch on doctrine and morals, or if it is, so long as he does not attempt to invoke the authority of his office to declare it to be true, he is simply wrong. No canonical process is required.
As for the situation in which the pope attempts to use his authority to declare as true something that is clearly contrary to doctrine and morals, he would have fallen into heresy and apostasy, and would have deposed himself.
I don’t know how recognition of this situation would work in practice, and probably not even the most learned of canonists would either, because the Church has never been faced with this event.
Some say that the Holy Spirit would prevent the Pope from abusing the charism of his office in this way, but this is to retreat into a pious truism without addressing the question.
There are cases in the past of a Pope being tried for heresy (often by another Pope), and a few where the College in Paris was called in to settle some things.
However, that was a long time ago.
I ask not to throw mud, but because having see such things in other church bodies, I hope that Catholics have a plan.