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Calcium carbonate, or `CaCO_3 ` is the chemical term for what is more commonly known as chalk (though not blackboard chalk, which is calcium sulphate). Google cites that calcium carbonate is
"a white insoluble solid occurring naturally as chalk, limestone, marble, and calcite, and forming mollusc shells and stony corals"
[For another definition, see also Academic Press Dictionary of Science and Technology, Christopher G. Morris, p. 340]
Calcium carbonate does not dissolve in water (is not soluble in water) but, like all carbonates, it reacts with acids. For example, in the natural lime cycle, rainwater runs through limestone and creates stalactites and stalagmites. This is because rainwater, through ` ``H_2O ` (water) combining with `CO_2 ` (carbon dioxide), becomes an acid, `H_2CO_3 ` (carbonic acid). This can react with the limestone (calcium carbonate) as it passes through, dissolving it very mildly and forming stalactites and stalagmites over long periods of time (years). Another example is the recommendation not to clean marble surfaces with lemon juice (containing citric acid) or vinegar (containing ethanoic acid) since these are acidic and act on the marble. (see first link below)
Now, ethanol as a solvent polarizes substances ionically less than water, so that since calcium carbonate dissolves very little in water it is even less soluble in ethanol. Ethanol also, like water, has a neutral pH of 7 so does not react on calcium carbonate as acid (such as lemon juice, or vinegar) would. It follows then that calcium carbonate would not be soluble in an ethanol and water mixed solution.
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