Pope Honorius was what is called a “heretic before the fact.” That means he believed heresy (namely the Monothelite heresy) before it was determined to be heresy.
He’s far from the only Catholic to have done so. St. Cyprian of Carthage (my favorite Early Church Father) was a heretic before the fact in his denial of the validity of Christian Baptism at the hands of heretics (he saw a defect of minister which does not exist).
But Honorius was not just an “ordinary” Saint - he was also a POPE. And he was a heretic before the fact.
He was not ONLY condemned (posthumously, and thus rather pointlessly) as a heretic by Pope Leo-2, but also by the (Ecumenical) Third Council of Constantinople:
…to Honorius some time Pope of Old Rome, as well as the letter of the latter to the same Sergius, we find that these documents are quite foreign to the apostolic dogmas, to the declarations
…we define that there shall be expelled from the holy Church of God and anathematized Honorius who was some time Pope of Old Rome, because of what we found written by him to Sergius, that in all respects he followed his view and confirmed his impious doctrines.
To Theodore of Pharan, the heretic, anathema! To Sergius, the heretic, anathema! To Cyrus, the heretic, anathema! To Honorius, the heretic, anathema! To Pyrthus, the heretic, anathema!
So, yes, the Catholic Church has had, at least, one heretical Pope (before the fact). Not just an overtly **sinful **Pope (we’ve had LOTS of those), but a
heretical Pope.
But this is the REALLY, REALLY important part: the Church does not teach that Papal infallibility means that a Pope cannot BE a heretic. It means that the Pope cannot TEACH heresy (in his capacity as Pope).
WHAT was the evidence that Constantinople-3 cited to prove his heresy? I have quoted it, but I will quote it again:
because of what we found written by him to Sergius, that in all respects he followed his view and confirmed his impious doctrines.
This was a private letter (which Honorius clearly never intended to become public record) of one heretic to another. This does not, in any way, constitute teaching with the authority of the Papal Office.
Popes can be (and have been) sinners. Popes can be (and have been) heretics. Popes CANNOT teach their sin or heresy as Catholic Doctrine. And none ever have.