Here's just my take on a what if Eragon stumbles into the world of the Dragon reborn. I decided I would take both stories from after their official conclusions so It will be full of spoilers, if you notice any errors I apologize feel free to message me, same goes for any thoughts, criticisms and Ideas cheers for reading.
Eragon eyes swept the horizon, it had been a eighteen months since he and Saphira said goodbye to their world and flew out to sea in search of a new place for dragons to start over. The ship pitched and rolled as waves the size of hills passed by. Eragon reached out with his mind, meditating on the difference between the expanses of water was so different from the glade in Du Weldonvardon but still just as complex. A smile pulled at the corner of his lips as he felt his companion shooting through the water catching fish as large as he was. Eragon couldn't help but be a little nervous Nïdhwalar and other creatures of the deep. But His mediation and her games were all that kept them sane during the long journey.
It was then that he spotted a green smudge on the horizon, "Land!" Eragon sent eagerly, Saphira erupted from the surface of the water and Eragon leapt from the deck and gracefully landed on her back a warm mirth and anticipation radiated through the bond between them.
Rand walked down the streets of Emonds Feild he suspected Perrin would have to change the name. The fields had long been cover by a hive activity. Loil and the Ogyr had begun working on a city in memorial of his victory over the dark one. Avindah had mentioned she had a vision of the two rivers becoming a thriving city.
For the time his peace held. The nations were just as volatile as they had been in ages past but fear of the Aile and the Seachean kept them from over stepping their bounds. Empress Foutona had been as good as her word though he heard from Elayne there had been harsh words between her and the new Amrylin. He was amused to hear that Cadusane had taken up the staff and stole.
Rand sighed, every time he thought of the Amrlyn his thoughts inevitably led to Egwene Al'vear and the others who had died in the last battle. As if the wounds in his sides were still there he ached for the ones who had fallen. Egwene's name had replaced Moiraine's at the top of his list right above Ilyena. Rand had insisted to Elayne if the was to be a statue of him, the list was to encircle the base there was a lot of "wool headed fool" from her but she agreed quickly. The Statue already stood completed; it seemed it was to be the centre piece of the new city.
Rand smiled and kept walking. He set off to see the world.
Eragon and Saphira skirted over many Islands but decided instead to find mountains to establish their new order "I wonder what kind of people we'll find here?" Eragon Mused watching, "Humans doubtless" Saphira remarked as the shape of a city emerged on the coastline "Orrmis always said your people arrived from across the sea. I wonder If there will be dragons?" "I doubt it." "I see a creature in the sky youngling." Eragon blinked then he too noticed a winged creature flying around the city. As they drew closer more and more of these creatures could into view at least a dozen. It was then that Eragon noticed they were all mounted by humans. The other thing that he noticed was that they were certainly not dragons. At first he mistook them for a Fanghur but the body wasn't snake like enough, these creatures were like small stupid dragons.
"we should head west for awhile and stay hidden" I can sneak into the city tonight and see what I can find out."