Bulk c-oriented CeF3 single crystals (sp. gr. P3¯c1) were grown successfully by the vertical Bridgman technique in a fluorinating atmosphere. A description of the crystal growth procedure and the solution of the difficulties during the growth process are presented in detail. The anisotropy of the mechanical, thermal and electrophysical properties were studied for the first time. The maximum values of the thermal conductivity coefficient (α = 2.51 ± 0.12 W·m−1·K−1) and the ionic conductivity (σdc = 2.7 × 10−6 S/cm) at room temperature are observed in the [0001] direction for the CeF3 crystals. The Vickers (HV) and Berkovich (HB) microhardnesses for the (0001), (101¯0) and (112¯0) crystallographic planes were investigated. The HB values were higher than the HV ones and decreased from 3.8 to 2.9 GPa with an increase in the load in the range of 0.5–0.98 N for the hardest (0001) plane. The {112¯0}, {101¯0} and {0001} cleavage planes were observed during the indentation process of the CeF3 crystals. The variability of Young’s, the shear modules and Poisson’s ratio were analyzed. A significant correlation between the shapes of the Vickers indentation patterns with Young’s modulus anisotropy was found. The relationship between the anisotropy of the studied properties and the features of the CeF3 trigonal crystal structure is discussed.