Within the density functional theory, the Hartree–Fock/Kohn–Sham-coupled perturbation method using the basis of localized orbitals, the gradient PBE functional with dispersion correction D3(BJ) and hybrid PBE0 and B3LYP functionals, the structural, dielectric, and piezoelectric properties of hexagonal alkali fluorocarbonates ABCO3F (A: K, Rb, Cs; B: alkaline earth (Mg, Ca, Sr) and d10 (Zn, Cd, Pb)) were evaluated. In the series of crystals, fluorocarbonates with lead have the highest values of the calculated components of the dielectric constant tensor, piezoelectric constants, and nonlinear optical (NLO) coefficients.