The 1111 compounds with an alternating sequence of fluorite and antifluorite layers serve as structural hosts for the vast family of Fe-based superconductors. Here, we use neutron powder diffraction and density-functional-theory (DFT) band-structure calculations to study magnetic order of Eu²⁺ in the [EuF]⁺ fluorite layers depending on the nature of the [TAs]⁻ antifluorite layer that can be non-magnetic semiconducting (T = Zn), magnetic semiconducting (T = Mn), or magnetic metallic (T = Fe). Antiferromagnetic transitions at T_N ∼ 2.4-3 K due to an ordering of the Eu²⁺ magnetic moments were confirmed in all three EuTAsF compounds. Whereas in EuTAsF (T = Zn and Mn), the commensurate k₁ = (½ ½ 0) stripe order pattern with magnetic moments within the a-b plane is observed, the order in EuFeAsF is incommensurate with k = (0 0.961(1) ½) and represents a cycloid of Eu²⁺ magnetic moments confined within the bc-plane. Additionally, the Mn²⁺ sublattice in EuMnAsF features a robust G-type antiferromagnetic order that persists at least up to room temperature, with magnetic moments along the c-direction. Although DFT calculations suggest stripe antiferromagnetic order in the Fe-sublattice of EuFeAsF as the ground state, neutron diffraction reveals no evidence of long-range magnetic order associated with Fe. We show that the frustrating interplane interaction J₃ between the adjacent [EuF]⁺ layers is comparable with in-plane J₁-J₂ interactions already in the case of semiconducting fluorite layers [TAs]⁻ (T = Zn and Mn) and becomes dominant in the case of the metallic [FeAs]⁻ ones. The latter, along with a slight orthorhombic distortion, is proposed to be the origin of the incommensurate magnetic structure observed in EuFeAsF.