Integrated sensing and communications (ISAC) is a key use case for sixth-generation (6G) wireless systems, where parametric channel estimation (PCE) plays a central role in enabling sensing, localization, and channel equalization in high-mobility scenarios. However, PCE is typically more computationally demanding than conventional channel estimation, which motivates the development of lower-complexity solutions. In this letter, we propose a fast PCE algorithm for time-varying and frequency-selective (TVFS) channels based on canonical polyadic (CP) decomposition and tensor processing, combined with ESPRIT-based initialization, component refinement, and exact line-search alternating coordinate descent. Two variants are presented: one for fully digital and another for hybrid receiver architectures. Numerical results show that the proposed method clearly outperforms a related CP-based baseline while achieving estimation performance close to a multiple-start SAGE benchmark at a substantially lower computational cost, with about one order of magnitude shorter execution time.