The story of Shakyamuni Buddha would have been spread about: that his royal father wished his son to succeed him, but a prophesy that he would become a religious figure made the father anxious. The father surrounded his son with all manner of sinful items and behavior and isolated him from any evils of the world that might provoke sympathy and caring. Despite these precautions, the son turned to religion and eventually became the Buddha.
This story would have been appealing and familiar to Christians: turning away from the pleasures and riches of a material life and embracing religion is the origin story of several saints. In fact, many details of the Buddha's origin (I have severely streamlined it) match uncannily to the life of a particular Christian saint, St. Josaphat.
I wrote a skeptical post years ago about St. Josaphat and the supposed connection to Buddha. Around the same time, a book was published that tracks the story of the Buddha as it raveled westward and was translated into different languages, with each new translation adding culturally significant details, until it reaches the Latin west adapted as the story of St. Josaphat. And that is how Buddha became a Christian medieval saint. The illustration shows Buddha on the left and St. Josaphat on the right.
Some think the Greek version was first created by John of Damascus, one of the Doctors of the Church such as Augustine of Hippo. I'll tell you more about him tomorrow.