Although His Holiness Pope Francis has a private or official email address, he does have a public email address. People who want to reach him through modern means are not reliant on snail mail, as he has an active social media feed.
How can you contact Pope Francis?
For contact with Pope Francis by post, the Vatican provides this address:
His Holiness, Pope FrancisApostolic Palace00120 Vatican City
Despite his lack of access to email, Pope Francis sees modern communication options as useful. When Apple CEO Tim Cook visited the Vatican in January 2016, Pope Francis released a message titled Communication and Mercy: A Fruitful Encounter for the 50th World Day of Social Communications. In it, he said that the Internet, text messaging and social networking are “gifts from God.”