The unique combination of excellent semiconducting properties in halide perovskites and the high stability and nontoxicity of oxide perovskites has led to a recent surge in interest in chalcogenide perovskite BaZrS3 for optoelectronic applications. However, to realize its potential in future device technologies, a comprehensive understanding of photoexcited carrier dynamics and transient optical response is imperative, yet it remains largely unexplored for BaZrS3. In this work, employing transient absorption spectroscopy, we have revealed that photoexcited carriers in epitaxial BaZrS3 nanofilms exhibit two exponential decay components relating to optical phonon cooling and interband recombinations. Meanwhile, our investigation unveils an intriguing transient nonlinear absorption phenomenon in BaZrS3, characterized by the ultrafast switching of the pump-induced transparency (i.e., the saturable absorption) to the absorption enhancement within a timescale commensurate with the measurement resolution (hundreds of femtosecond). This study provides crucial dynamic insights essential for leveraging chalcogenide perovskites, such as BaZrS3, in the development of advanced optoelectronic devices.