Paula Podest Ruiz, 39, and Carlos Ciuffardi Elorriga, 41, were on board and they started chatting with the Pope, who was travelling from Santiago to the northern city of Iquique in Chile.
They'd been unable to follow it with a church wedding, but had been unable to because it had been destroyed by an earthquakr.
According to Ciuffardi, Francis told them what happened "was historic", because "never has a Pope married a couple on a plane". He also revealed what the pope told them, "This is the sacrament that is missing in the world, the sacrament of marriage".
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"We told him that we are husband and wife, that we have two daughters and that we would have loved to receive his blessing", Ciuffardi said.
The couple explained their situation to Pope Francis, and asked if he could bless their marriage. "All of a sudden, he asked us if we were married for the Church too", Ciuffardi told reporters later on the plane, according to Reuters.
A stunned Podest was almost speechless during the remaining hour on the flight as she recounted the story to the 70 or so journalists who travel with the pope on his foreign trips.
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"He liked us and he asked, 'Do you want me to marry you?'" Ciuffardi recounted. Ciuffardi then asked Ignacio Cueto, the CEO of the airline, to become the witness.
Since they didn't have an official marriage certificate to sign, Pope Francis asked the cardinals with him to draft one, so they grabbed a piece of blank copy paper and each signed their names and what role they played in the ceremony.
Referring to the rings, Francis jested that they shouldn't be too tight, because "they would be a torture", nor too loose, because they might lose them.
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He also said that while he respected the result of the June 23 referendum, he would "love" to welcome the United Kingdom back. "This special way should be consistent with the preservation of the single market and our collective interests", he said.
Pope Francis brought his motorcade to a halt to check on a police officer who fell from her rearing horse along the route.