Reread Franzelin. I don't expect you to make any progress though, because your attitude is not one that is conducive to learning anything.
Franzelin is saying that Catholics were excused subjectively for following anti-popes in good faith during a time when the universal Church was in complete legitimate confusion over which of three rival claimants were Pope.
As your quite by Franzelin begins, these same Catholics believe in the perpetual existance of a human being in the apostolic see, at the time it was just not clear which man than was.
This is totally different from a Catholic today believing VCI's claim that Peter will have pepetual successors is crap and that the current Pope recognized by the universal Church is not actually Pope.
The first position was obviously reasonable due to the circuмstance. The second position is patently absurd. I'll let Ferrara explain....
A Patent Absurdity
That the premises, and thus the conclusions, are demonstrably false will be shown later. But even without such a demonstration, it must be stressed at the outset that the sedevacantist thesis is plainly untenable, because when all is said and done the thesis comes down to the following claim: that since 1958 the entire membership of the Catholic Church has been adhering to a series of impostor popes and a hierarchy of impostor bishops, except a few sedevacantists who alone have noticed what is "manifest" about these ecclesiastics — that they are all formal heretics. For the Church’s entire membership to adhere for nearly half a century to five consecutive heretical, impostor popes and an impostor episcopacy would make a mockery of the promises of Christ to His Church that "the gates of hell shall not prevail against it" (Matt. 16:18) and that He will be with His Church "all days unto the consummation of the world" (Matt. 28:20). Without the Pope at its head and bishops in communion with him, the visible Church would cease to exist, and Christ would have been made a liar.
Granted, it may well be that the Church is ultimately reduced to a very tiny remnant by the time Antichrist appears and asserts himself. But that remnant will still have a Pope at its head and some number of bishops in communion with him. Otherwise that remnant would not be the Church, but a headless and diffuse "body of believers," just as the Protestants imagine the Church to be. Quite simply, if there is no Peter, there is no Church. As Pope Leo XIII taught in his monumental encyclical on the Church, Satis Cognitum: "It is clear that by the will and command of God the Church rests upon St. Peter, just as a building rests on its foundation. Now the proper nature of a foundation is to be a principle of cohesion for the various parts of the building. It must be the necessary condition of stability and strength. Remove it and the whole building falls."3