The legitimacy of capital punishment has been upheld in the Bible, all the Church Fathers, the Doctors of the Church (including St Augustine and St Thomas Aquinas) and the Council of Trent. It forms part of Catholic Dogma we are required to accept. Furthermore the Waldensian Heretics, who opposed war and the death penalty, after their uprising was defeated, were required to take an oath stating inter alia that-
“Concerning secular power we declare that without mortal sin it is possible to exercise a judgment of blood as long as one proceeds to bring punishment not in hatred but in judgment, not incautiously but advisedly” (Denzinger 425)
That is not to say that the state, having the right to impose the death penalty, should always make use of it. There are prudential arguments as to why the use of the death penalty should not be used today, which Catholics will likely continue to debate forever.
Pope Francis is within his rights (as did Pope St Nicholas, Pope St John Paul II and Pope Benedict XVI before him) to teach prudentially that the circumstances that would justify use of the death penalty are not present in our society (which is where the term “inadmissible” comes from). But he can never teach that it is intrinsically evil and inherently wrong, or that the state has no right to use it under any circumstances, as that would contradict 2000 years of Church teaching.
Furthermore as for it being licit to disagree with the Holy Father on this, Pope Benedict XVI (when he was still Prefect of the CDF) stated that -
“Not all moral issues have the same moral weight as abortion and euthanasia. For example, if a Catholic were to be at odds with the Holy Father on the application of capital punishment or on the decision to wage war, he would not for that reason be considered unworthy to present himself to receive Holy Communion. While the Church exhorts civil authorities to seek peace, not war, and to exercise discretion and mercy in imposing punishment on criminals, it may still be permissible to take up arms to repel an aggressor or to have recourse to capital punishment. There may be a legitimate diversity of opinion even among Catholics about waging war and applying the death penalty, but not however with regard to abortion and euthanasia”.
For a more in depth view of this issue I would strongly recommend the comments of Father Thomas Petri OP, who gave an excellent summation on this issue on EWTN.