Who said he had an agreement with Real? Marca.
We can't be sure of anything, but he chose PSG in the end, and that's a fact. He didn't even choose them because of the salary (his wage were only discussed between PSG, and his father last wednesday.) Mbappe said it after the game with France, he chose PSG because he knows he will play there in the main 11.
My personal opinion would be that he likes Real, sure, but he didn't want to start from scratch on the bench trying to win a spot. Maybe he was scared to fail? Whatever, to be honest I'm just happy he said No to Real, and we know he said No to them, and that's all that counts to me.
Why would he refuse? It would not be the first time a player who fancied a club as a kid joins the rival once an adult.
PSG won't let his contract runs out, they are not stupid. All we need is to be in good terms with them.
1- Barca board changes.
2- Perez, and PSG honeymoon is over as Perez is angry at them because of Mbappe, and PSG is angry at Perez because he's part of the clubs that try to make them banned from CL according to L'Equipe.
To me all sounds good for a future transfer here. But maybe I'm too optimistic.