Will mankind on earth reattain the original state of Adam and Eve? Adam and Eve, were constituted in an original "state of holiness and
  justice".250 This grace of original holiness was "to share in. .
  .divine life" CCC375


Now, I've heard a priest say that through Christ's death on the cross all of humanity will go back to the original state. I imagine this as if mankind's goal was to return back to Adam's original state of holiness. And when looking at history, we can see that societies are becoming softer and more authentic despite all the evil happening around us. Thanks to new technologies, humans are more open and transparent, which changes our mentality.

My question is: Will this happen on Earth, or is it meant for after the Second Coming and Resurrection? What Catholic teaching is the priest referring to?
No, all of mankind will not return to the original state of Adam and Eve.

The Origenists' heresy of apokatastasis or doctrinal universalism claimed "that hell is essentially a kind of purgatory in which sins are expiated, so that eventually everyone will be saved."

The following proposition was condemned as heretical in 543 A.D. (Denzinger 411):


  the punishment of devils and wicked men is temporary and will eventually cease, that is to say, that devils or the ungodly will be completely restored to their original state


Evolutionists like the heretic Teilhard de Chardin, S.J., think mankind naturally evolves toward greater perfection, but this is a denial of original sin. Adam and Eve started out in a state of perfection and devolved after they sinned, the opposite of what evolutionists claim. God's supernatural grace is necessary for restoring the original order, but not everyone corresponds with His grace.