Using first-principles calculations, the structural, vibrational, and electronic properties of single-layered calcium fluoride (CaF₂) are investigated. The dynamical stability of 1T-CaF₂ is confirmed by the phonon dispersions. Raman active vibrational modes of 1T-CaF₂ enable its characterization via Raman spectroscopy. In addition, the calculated electronic properties of 1T-CaF₂ confirmed insulating behavior with an indirect wide band gap which is larger than that of a well-known single-layered insulator, h-BN. Moreover, one-dimensional nanoribbons of CaF₂ are investigated for two main edge orientations, namely zigzag and armchair, and it is revealed that both structures maintain the 1T nature of CaF₂ without any structural edge reconstructions. Electronically, both types of CaF₂ nanoribbons display robust insulating behavior with respect to the nanoribbon width. The results show that both the 2D and 1D forms of 1T-CaF₂ show potential in nanoelectronics as an alternative to the widely-used insulator h-BN with its similar properties and wider electronic band gap.