An idea that I have involves Louis VIII replacing John as king of England. The feudal barons pissed off at John used him as an alternative (they didn't have a proposed successor IOTL, which makes it very unusual) in exchange for him signing the Magna Carta. He was literally the only person with legitimacy. He would later also become the king of France, thus starting a union between the two.
As long as the barons' rights were respected in the Magna Carta, they were content and wouldn't threaten rebellion. Since the king would be forced to move to Paris to properly rule both kingdoms, he wouldn't have to be involved in English affairs much anyway.
A major problem, I experience is trying to make the barons receptive to the idea of a man native to France, whom they had been warring with for thirty years. Butterflying the wars would end up butterflying the reasons the barons rebelled in the first place. Could their rebellion end up losing legitimacy since they don't have a potential successor? Or perhaps some actions of John would force them to choose an alternative?
And what would this theoretical country be called?
I appreciate any input.