Feudalism is a form of governance, not an economic theory. It might replace our current representative republic, but our current economic system is going to have to be replaced by another economic system.
Our current economic system is indeed Free Market Capitalism - in the only form it can ever exist - a compromised one. True "Laissez-faire" Capitalism can never exist in practice because it is too virulent to thrive - like Ebola in its most aggressive form, it kills the host before it has a chance to propagate itself. Since no halfway sane society would for tolerate for very long the gross abuses and injustices that naturally result from too much capitalism, the state will always (indeed must always) step in and alleviate those abuses by restraining Capitalism (or more accurately, restraining Capitalists) by way of anti-trust laws, child labor laws, union laws, workplace regulation laws, etc, etc, etc... Put simply, Capitalism always leads (paradoxically some might think, but not really) to some form of Socialism (as described by Belloc in The Servile State). As Joe Z states, private ownership in this nation is ultimately controlled by the State - and yet the State is itself in the thrall of International Bankers via the Federal Reserve...
As Chesterton rightly pointed out, the problem with too much Capitalism is that it results in too few Capitalists. And if we're positing a post-collapse return to Catholic Tradition and Catholic Governance (in other words, a much needed return of Western Civilization to Sanity), then I would venture to guess that we'd adopt an economic theory that is also in line with Catholic morality. The definitive text on Catholic morality with respect to economics remains Pope Leo XIII's Rerum Novarum, and the only economic theory that can claim to have been designed specifically to conform to that definitive statement of Catholic economic morality is the aforementioned Messrs. Belloc and Chesterton's Distributism (also known as Proprietorism). Therefore, that would be the replacement I would put forth for our current lamentable condition of State Sponsored Usury known commonly as "Capitalism."