Electronic distortions, which are inherent in the oxide fluoride anions [MOF] (M = Nb and Ta), provide an origin of polar molecular arrangements for the development of new polar second-harmonic-generating, piezo-, pyro- and ferroelectric materials. It is still a challenge to expand this approach to the realm of metal-organic polymers, while insufficient control over the environment of the [MOF] units results in their orientational disorder and loss of polarity. The structures of catena-poly[[tris(3,4,5-trimethyl-1H-pyrazole-κN)copper(II)]-μ-oxido-[tetrafluoridoniobium(V)]-μ-fluorido], [CuNbFO(CHN)], (I), and its isostructural pentafluoridooxidotantalate(V) analogue, catena-poly[[tris(3,4,5-trimethyl-1H-pyrazole-κN)copper(II)]-μ-oxido-[tetrafluoridotantalum(V)]-μ-fluorido], [CuTaFO(CHN)], (II), are the first examples of the strict orientational order of [MOF] (M = Nb and Ta) in one-dimensional coordination chains. A primary factor for the exact discrimination of one orientation of the anion over the other is strong and shape-selective multiple interactions of [MOF] with the inherently acentric CuL platform, with a set of two coordination and three N-H...F hydrogen bonds. In (I) and (II), the Cu ions exhibit distorted square-pyramidal fivefold coordination formed by three pyrazole N atoms and the oxide O atom, defining the equatorial plane, and the anionic bridging F atom (which is trans with respect to the M-O bond) residing in the apical position. The inorganic bridges connect CuL moieties into polar zigzag chains; the bulk polarity of the structure is eliminated by an antiparallel alignment of the individual chains. These chains are further connected through C-H...F hydrogen bonding and very weak C-H...π interactions of the organic ligands.