New BiS2-based layered compound Eu3Bi2S4F4 has recently been reported to exhibit superconductivity with a transition temperature of 1.5 K using polycrystalline samples. Here we report measurements of electrical resistivity ρ, magnetization M, and specific heat C of Eu3Bi2S4F4 single crystals. At the antiferromagnetic transition temperature of 2.17 K, C(T) shows a sharp λ-type peak, suggesting the existence of strong Eu magnetic moment fluctuations due to the quasi-two-dimensional nature of the Eu-ion lattice in Eu3F4 block layers. The average Eu-ion valence of +2.19, determined from the Schottky-type 4f-electron contribution to C(T) and M(T,H), indicates the self-doped electron density in BiS2 layers due to the Eu mixed valence to be 0.285 electrons per Bi site. It has been revealed, however, that ρ(T) shows an anomalous nonmetallic behavior with ∼1/T3 dependence without any sign of superconductivity, in marked contrast to a metallic behavior in the polycrystals. This behavior suggests an unconventional electron-localization mechanism working in the single crystals, possibly caused by Eu2+/Eu3+ distribution (or fluctuations) and/or lattice instabilities inherent to BiS2 layers. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.