We present the morphological evolution and fractal characterizations of CaF2 thin-film surfaces modified by bombardment with 100 MeV Au+8 ions at various fluences. Atomic force microscopy (AFM) combined with line profile and two-dimensional power spectral density (2D-PSD) analysis was utilized to investigate the evolution of surface morphology as a function of fluence. The AFM images were utilized to investigate the relationship between fractal dimension, roughness exponent, lateral correlation length, and ion fluence. The surface erosion owing to sputtering was depicted using Rutherford backscattering spectrometry. The structural characteristics' dependency on fluence was explored with the help of glancing angle x-ray diffraction measurements on virgin and irradiated samples. Tensile stress calculated using a peak shift in the glancing angle x-ray diffractogram showed an increase in tensile stress with fluence that caused the surface to crack after the fracture strength of the surface was crossed. 2D-PSD analysis signified the role of sputtering over surface diffusion for the observed surface modifications. Fractal dimensions first increased and then decreased with ion fluence. The lateral correlation length decreased, while the roughness exponent increased with fluence after the threshold value.