Question: Did Pope Francis say that hell doesn't exist?
Short answer: No. This is fake news.
Longer answer: The apparent source of this question comes from 94 year old Italian journalist Eugenio Scalfari who, in conversation with Pope Francis, asserted this:
Francis was quoted as saying of those who die in a state of mortal sin: “They are not punished. Those who repent obtain God’s forgiveness and take their place among the ranks of those who contemplate him, but those who do not repent and cannot be forgiven disappear. A hell doesn’t exist, the disappearance of sinning souls exists.”
This is merely the assertion of Scalfari, as he recollects a conversation they had. There is no recorded transcript of this. Scalfari acknowledges that he does not take notes during these meetings, and is merely going by his memory of this discussion he and Pope Francis had. Scalfari has said: “These are not interviews, these are meetings, I don’t take notes. It’s a chat.”
In fact, Pope Francis has upheld, affirmed and professed the teachings of the Church on hell on numerous occasions. In May of 2017 at the 100th Anniversary of Our Lady's appearance at Fatima, he said:
"Our Lady foretold, and warned us about, a way of life that is godless and indeed profanes God in his creatures...Such a life, frequently proposed and imposed, risks leading to hell."
And during a prayer vigil in 2014, he addressed members of the Italian mafia saying:
"...while there is still time, so that you do not end up in hell. That is what awaits you if you continue on this path.” (bold mine)
Also, I've been in numerous discussions with people who pose the above question in a slightly different way: "Why did the Catholic Church change its teachings on hell?" When I ask what they're referencing, they say: "Your Pope just denied that hell exists". This demonstrates an egregious ignorance among so many people who think that everything the Pope says is infallible, definitively pronounced Catholic dogma. In fact, what a pope says, in conversation, is NOT THE SAME THING as a pope speaking officially. Even if a pope is preaching a homily, he is not speaking from the Office, from the Chair; his words are to be taken with the wisdom of a theologian, and ought to be considered and thoughtfully digested...but they are not the same thing as a solemn, formal declaration of Catholic dogma.
Indeed, even if a pope writes a book on theology, we ought not mistake this book for Catholic doctrine. Pope Benedict XVI says as much in the preface to his book on Jesus:
He writes, "Of course, it goes without saying that this book is absolutely not a magisterial act, but is only the expression of my personal search for the face of the Lord (Psalm 27:8). So everyone is free to disagree with me."