Pope Francis has ties to the eastern churches. In Argentina, he was the ordinary for Eastern Catholics (Eastern Catholics are Catholics with many of the same traditions and customs as the Orthodox Churches, but are in union with the Pope). The Gospel at the Mass will be proclaimed in Greek, the historical language of the East, instead of Latin, the historical language of the West.
Here is what Jimmy Akin says about this:
One should not view this as the pope dissing Latin. They're going to be using lots of Latin in this Mass.
As papal spokesman Fr. Lombardi noted:
“Latin,” Fr. Lombardi said, “is already abundantly present in the other prayers and Mass parts.”
Furthermore, they announced:
The Gospel will be proclaimed in Greek, as at the highest solemnities, to show that the universal Church is made up of the great traditions of the East and the West.
Proclaiming the Gospel in Greek is not an innovation here. It's something they already do on special occasions to show the Church's universality.
So it's in accord with precedent.
It's also not surprising that they would exercise this option here since this is already a Solemnity (St. Joseph's day), since it's a very solemn Mass (a papal inauguration), since Pope Francis has for years been an ordinary for Eastern Catholics in Argentina (Greek being a primary liturgical language in the East), and--in an extraordinary ecumenical gesture that hasn't happened in almost 1,000 years--the Patriarch of Constantinople (Bartholomew I) is going to be attending.