Will NaF + CaCO3 precipitate much CaF2?

If I mix sodium fluoride, calcium carbonate powder, and water, under what conditions (if any) would there be an equilibrium?

I.e. assume we start out with fully dissociated $\ce{Na+(aq) + F-(aq)}$, because it's fairly soluble. But when I add the $\ce{CaCO3}$, it's only slightly soluble, so assume an excess of solid $\ce{CaCO3}$ and a small amount dissolved.Will that be stable with $\ce{NaF}$ concentration much greater than the saturated concentrations of $\ce{CaCO3}$, or will $\ce{CaF2}$ start to precipitate, and will it continue until exhaustion of a reactant, or reach equilibrium?

I'm wondering if it's the relative solubilities of $\ce{CaCO3}$ and $\ce{CaF2}$ that will drive the equilibrium (if that's what it is) one way or the other. I can't work out how to apply the theory of an equilibrium constant because of the excess solid reactant and corresponding possible precipitate messes up how concentrations balance out in a normal equilibrium… And I'm wondering if the absolute concentration of $\ce{NaF}$ effects things as well.

Any pointers appreciated. Or even some jargon to say what this kind of reaction is called.