In practice there are many mixed forms of "democracy," "markets," and "socialism."
But the idea there there is somehow an interdependence between a "free market" and "political freedom," is, in my view, utter propagandistic nonsense.
The easiest error to point out is the idea of a "free market." There have always been "markets" but from the time of the East India Company up until the era of global banks, pharmaceutical patents, and multinational oil companies there is no "market" that is not founded, determined, and actively conditioned by state governments.
The enormous sway of military defense contracts, the supplementation of corporate costs in everything from worker education and infrastructure to research, the massive tax costs entailed by registering, securing, recording, and protecting "property" of all sorts means that there is absolutely nothing "free" and "natural" about pricing. The most comprehensive example is simply the tax-bonded funding and private bank "pricing" of money credit itself, on which every other "price" is based. The most important U.S. historical example is agriculture, where extensive price intervention and government support was absolutely necessary to stabilize American farming, research, shipping, and food supply.
Markets are creations of governments, and governments grow as markets grow. Markets, as well as political or military power, can also place severe constraints on "democracy." The ancient Athenians might be astonished at how few things we can vote on and that only "representatives" can actually vote on legislation. Other ancient governments might note that these "representatives" do not represent economic classes, but only regions. In sum, the the number of things we can actually vote on is extremely limited, often by markets interests, as is evident in things like wage laws, corporate legal exemptions, extended copyrights, and pharmaceutical patents.
In history and practice there are many complex interactions of markets and democracy. To some extent they are interdependent, and it will be interesting to see how the China variation emerges. But the rigid linkage of "free" markets and political "freedom" is largely a Cold War goblin story, and it is always far easier and more controlling to erode the effectiveness of voting than to overtly curtail it.