A breakout tournament at a major would catapult him into superstardom - Sancho isn't really famous in England yet and only those following his career up to this point could tell you anything about him. Post Euros, he could well be a household name, not just in England but across Europe/world. It would also remove doubt that this player is the real deal the majority of those watching his career unfold, believe that he is. Obviously, part and parcel of that will be image rights and sponsorship potential going through the roof as clubs are then looking at buying an already established star, which comes at a premium.
It wouldn't be a surprise if he also then attracts serious interest from clubs who usually wait for the next stage of development (him doing the same things in a stronger league) as Real - and to a lesser extent, Barca - are wont to do, which changes the train of thought of him going back to the EPL by default as many seem to think will be the case.
The line of thought since Sancho came on the scene was him maintaining his level and showing consistency to then be worth the touted fees, but he seems to be developing further now and there's not much left for him to do in the Bundesliga, so the growth in terms of his worth, is going to come from outside of it [Bundesliga] by way of European competitions at both club and country level.
It wouldn't be too dissimilar to someone like Bale, I suppose, as he tore up the Premier League, but it was his performances outside of it that triggered all the hype and predicated a giant moving for him on an astronomical wage and transfer fee. You could also throw someone like Rooney into that kind of mix, as it was the Euros that triggered Newcastle, and in turn, our, move for him on an enormous wage and transfer fee (for a teenager) at the time. Both of the aforementioned became superstars because of Europe (in one form or another) and it could well be the case for Sancho, too - if we are indeed witnessing the upward trajectory of one of the world game's best.