If it turns out there really is no free will. What will happen? Do we get a kind Utopia? Or fascism where you are mistreated based on your lot in life?
There's no functional difference, unless you can accurately predict someone's actions, and to do that you'd need to predict the environment in which someone is making choices as well, which requires omniscience. So, there's no functional difference.
Remember the reasons we have punishments? To discourage further misdeeds. Also, to restore justice by inflicting suffering on those who deserve it. Punishments would still be dished out for pragmatic reasons, but retributive punishment would be rendered entirely meaningless.
It would also shatter all sense of acomplishment an individual could have. All that would be left is maybe a perverse pride in knowing you where born "better" than others.
I don't think society would survive if it was a common knowledge.
Like I said, how can you prove that free will exists now? We could very well already live in your scenario, and the world isn't ending because of a lack of free will (if it doesn't exist). I mean, it is ending, but not because of free will or the lack thereof.