I'm not sure specifically who Jon Franklin is without more context. He could be an ordinary person with a passion for sharing true stories, or perhaps a professional storyteller, journalist, or writer.
There could be a wise old wizard who gives Jon advice on how to hatch and take care of the dragon. Maybe there's also a rival of Jon's who is jealous of his discovery and tries to steal the dragon egg.
He could meet some of the last remaining Valyrian descendants. They might be hiding in the ruins, still holding on to their ancient knowledge and traditions.
It's interesting because it can explore different aspects of their characters. For example, how their relationship might change if they were in different situations, like facing a common enemy or having to make difficult decisions together. It gives a new perspective on their individual personalities as well.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
Arya could be a popular character. She might be the fun - loving aunt who teaches the baby some cool combat skills in secret, much to Jon and Sansa's initial dismay but later acceptance. She could bring a sense of adventure and a different perspective to the baby's life.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.