The meeting took place last Thursday, the Solemnity of the Assumption, according to various media reports.
The Vatican did not publicise the meeting and did not provide any details about the encounter.
Sánchez posted pictures of the meeting on her Instagram account.
"It was an honour for Jeff and I to spend time with His Holiness at his home in the Vatican," she wrote about the meeting with the head of the church.
"His wisdom, warmth and humour were deeply touching."
Francis reminded her not to take life too seriously and to keep a light heart.
Bezos and she are grateful "for this incredible blessing and the gentle wisdom he has shared with us".
Sánchez also commented on the topics of the conversation in her Instagram post.
"We also spoke about the urgent need for climate action, an issue that is as close to his heart as it is to ours," she wrote.
Francis' belief in finding beauty and meaning in all actions touched her deeply, according to Bezos' fiancée.
She also praised the Pope's recently published letter"On Literature in Education".
"I think it's great that he encourages priests to read poetry and literature in order to stay connected to the human spirit," said Sánchez.