This work reports the excitation and luminescence spectra at T = 9 K of the Mn2+-doped RbCdF3, RbCaF3, and CsCaF3 fluoroperovskites. A Mn2+ concentration down to 400 ppm has been detected. The present data together with those available for KMgF3:Mn2+, KZnF3:Mn2+, KMnF3, and RbMnF3, allow us to explore the variations of the zero-phonon line (ZPL) and the Stokes shift [associated with the Mn2+ luminescent 4T1g (G) --> 6A1g (S) transition] along the whole series of cubic fluoroperovskites doped with Mn2+ in order to investigate their dependence with the Mn-F distance, R. The experimental variation of the ZPL energy measured in the 206-215 pm range is E(ZPL) = -21 305 + 187R (pm). This strong dependence of ZPL upon R allows one to measure Mn-F distances along the series of fluoroperovskites with accuracies of better than 0.001 angstrom, thus improving by more than one order of magnitude the extended x-ray-absorption fine structure resolution. Furthermore, this sensitivity is extended down to 10(-4) angstrom when we analyze the variations deltaR induced by pressure in a given system. As regards DELTAE(s), the present results on Mn2+-doped fluoroperovskites demonstrate an increase of the Stokes shift when R increases. This behavior is explained to be related to a Gruneisen constant gamma(a1g) corresponding to the symmetric mode of the complex. The value of the constant is greater than 1.9, in agreement with calculations on divalent transition-metal complexes like MnF64- and VF64-. The importance of the present results for the observation of luminescence through the full series of Mn2+-doped fluoroperovskites is also discussed.