Before discerning his vocation to priesthood and religious life, a young Jorgé Mario Bergoglio studied to become a chemist, earning a master's degree in the subject from the University of Buenos Aires. Hence, he is familiar with the term poly- or multivalence, which is a term that is also used in logic, music, and medicine. As a non-scientist (but one who has studied logic), as I grasp it, in chemistry a "valence" refers to the number of valence bonds a given atom has formed, or can form, with one or more other atoms. In logic polyvalence refers to inexact, or approximate, reasoning. In other words, it is not binary. In either case, I think that this is the best we can do right now when discerning what his choice of the name indicates. This seems to suit his character as he is both quiet, unassuming, and simple as well as firm, decisive, and eloquent when he speaks.
In the true Catholic spirit, I have to go with Assisi/Xavier/de Sales, and/and/and, not either/or/or. It seems to me that the thread that weaves together the three Francises is being a missionary. This also links his papacy, at least to some extent, to that of Benedict XVI. Francis of Assisi, a missionary whose task, given him by our Lord, was to rebuild, that is, reform the Church. St. Francis Xavier who traveled far and died on Shangchuan Island, where he was waiting to continue his missionary journeys by taking the Gospel of Jesus Christ to the Chinese mainland. His other missionary destinations included Japan, Indonesia, and India. St. Francis de Sales, of course, was the Counter-Reformation bishop of Geneva, the city of Calvin, a master communicator, and so also a missionary who led many back to the Catholic faith.
In his brief remarks, he said: "And now let us begin this journey, the Bishop and people, this journey of the Church of Rome which presides in charity over all the Churches, a journey of brotherhood in love, of mutual trust. Let us always pray for one another. Let us pray for the whole world that there might be a great sense of brotherhood . My hope is that this journey of the Church that we begin today, together with help of my Cardinal Vicar, be fruitful for the evangelization of this beautiful city." Being a missionary, I can only take him to mean ab urbe, ad mundi (i.e., from the city to the world).
I loved that he led us in prayer for our beloved Benedict and that he asked us to pray for him before he blessed us.
I know from reading the late Peter Hebblethwaite's biography Paul VI: The First Modern Pope that Papa Montini was haunted by a verse from the Gospel According to St. John, something Jesus says to Peter after "the Rock's" threefold confessio in answer to the Lord's persistent question "do you love me?" and after telling Peter "Feed my sheep"- "'Amen, amen, I say to you, when you were younger, you used to dress yourself and go where you wanted; but when you grow old, you will stretch out your hands, and someone else will dress you and lead you where you do not want to go.' He said this signifying by what kind of death he would glorify God. And when he had said this, he said to him, 'Follow me'" (John 21:15-19). In light of this, let's commit to praying for our Holy Father daily.