Archbishop Lefebvre probably wavered a little on the question. Most of the time, His Grace was firmly against SVism. At certain times, he was unsure, true; yet, at other times, +ABL himself clearly expressed the idea, for e.g. on March 9 1980: "Archbishop Lefebvre's attitude was made very clear in a letter to the Sovereign Pontiff dated 8 March 1980. It reads as follows:
Most Holy Father,
To put an end to some rumors which are now spreading both in Rome and certain traditionalist circles in Europe, and even in America, concerning my attitude and my way of thinking with respect to the Pope, the Council, and the Novus Ordo Mass, and fearing lest these rumors should reach Your Holiness, I may make so bold as to reaffirm my consistent position.
1. I have no reservation whatsoever concerning the legitimacy and validity of your election, and consequently I cannot tolerate there not being addressed to God the prayers prescribed by Holy Church for Your Holiness. I have already had to act with severity, and continue to do so, with regard to some seminarians and priests who have allowed themselves to be influenced by certain clerics who do not belong to the Society.
2. I am fully in agreement with the judgment that Your Holiness gave on the Second Vatican Council, on 6 November 1978, at a meeting of the Sacred College: "that the Council must be understood in the light of the whole of holy Tradition, and on the basis of the unvarying Magisterium of Holy Mother Church.
3. As for the Novus Ordo Mass, despite the reservations, which must be shown in its respect, I have never affirmed that it is in itself invalid or heretical.
I would be grateful to God and to Your Holiness if these clear declarations could hasten the free use of the traditional liturgy, and the recognition of the Society of St. Pius X by the Church, and likewise of all those who, subscribing to these declarations, have striven to save the Church by perpetuating its Tradition.
I beg Your Holiness to accept my profound and filial respect in Christo et Maria.
+ Marcel Lefebvre
Anyway, that is a distinct question. Let's even put aside Pope John Paul II and Pope Benedict XVI for a minute, and focus solely on Pope Paul VI and Pope Francis for now.
1. Was Pope Paul VI Universally Recognized by the Teaching Church in 1965? Rev. Fr. Francis Connell, editor of the American Ecclesiastical Review after Msgr. Fenton, and personal friend of his, says that he was. "The whole Church, teaching and believing, declares and believes this fact, and from this it follows that this fact is infallibly true." This was in December 1965. What follows from this? That the sede-vacantist explanation of the Second Vatican Council is necessarily incorrect.
2. Is Pope Francis Universally Recognized by the Teaching Church in this year of Our Lord 2020? To answer that question, we have to first ask and answer, where is the Teaching Church today? The teaching Church, the Catechism of Pope St. Pius X, and most Theologians will say, continues in Bishops appointed by the Pope to Office. Thus, either there is no teaching Church, which means the Church has defected, or only the Bishops appointed by the last 6 Popes constitute the teaching Church. Then, all these Bishops, who number about 5000+, both daily while offering Mass, and also when they would have received their Papal Mandate for appointment/consecration, manifested and do manifest their recognition of the Popes as Popes. Even Cardinal Burke recently said, he recognizes the Pope, prays for him as Pope in the Mass, and that this is not something he does lightly, but only upon careful reflection.
Pope Benedict XIV teaches us, "But however it may be with this disputed point of ecclesiastical learning, it suffices Us to be able to state that a commemoration of the supreme pontiff and prayers offered for him during the sacrifice of the Mass is considered, and really is, an affirmative indication which recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter, and is the profession of a mind and will which firmly espouses Catholic unity. This was rightly noticed by Christianus Lupus in his work on the Councils: “This commemoration is the chief and most glorious form of communion” (tome 4, p. 422, Brussels edition). This view is not merely approved by the authority of Ivo of Flaviniaca who writes: “Whosoever does not pronounce the name of the Apostolic one in the canon for whatever reason should realize that he is separated from the communion of the whole world” (Chronicle, p. 228); or by the authority of the famous Alcuin: “It is generally agreed that those who do not for any reason recall the memory of the Apostolic pontiff in the course of the sacred mysteries according to custom are, as the blessed Pelagius teaches, separated from the communion of the entire world” (de Divinis Officiis, bk. 1, chap. 12)." https://www.papalencyclicals.net/ben14/b14exquo.htm
Does the Episcopal College, at the current time, pray for and commemorate the Pope as Pope in the Mass? If yes, then this is a sign that he is truly Pope, because by it, the Church "recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter" and that Her recognition, as Fr. Dom Prosper Gueranger says, "is a proof that, from that moment at least, the occupant of the Apostolic See is as such invested by God himself.” (Abbot Guéranger, O.S.B., The Liturgical Year , Vol XII, pg. 188)"