That the femtosecond laser pulses irradiate metallic materials thereby inducing ultrahigh strain rates, is an important experimental approach to studying the material behavior under extreme conditions. Femtosecond laser-generated shock waves in metal films have rise times of several picoseconds, the corresponding diagnostic technique is required to work with a higher time resolution, which makes the experimental measurements difficult. Chirped pulse spectral interferometry (CPSI) possesses capabilities of ultrafast time resolution and continuous measurement, thus it provides a diagnostic technique for studying the ultrashort shock wave. In this article, we carry out an experiment on femtosecond laser driven shock wave in copper film and the measurement by CPSI. Laser pulse of 25 fs duration at the central wavelength 800 nm is used, the tested samples are copper films of (5025) nm in thickness fabricated by electron beam sputtering deposition onto cover slip substrate of 180 m in thickness, pump beam focuses onto front surface of the copper film through the transparent substrate and this laser intensity is 2.31013 W/cm2. Chirped pulse spectral interferometry is used to detect the movements of the free rear surfaces of the copper films with temporal and spatial resolution. In the spectral interferometry, linearly chirped pulse is required and obtained by stretching the femtosecond laser pulse with a pair of gratings. The relation between frequency and time of the chirped pulse is accurately measured using asymmetric spectral interference method, which is required for explaining the experimental data. Since CPSI is a single shot diagnostic technique, we obtain the displacement and velocity history of the free rear surface with picosecond time resolution in a single measurement. From the results, the average shock velocity is calculated to be (5.60.2) km/s and the shock wave rise time is determined to be 6.9 ps. According to the shock wave relations, impact pressure and strain rate in the copper film are (57.18.8) GPa and 8109 s-1 respectively, the strain rate is so high that it is hard to achieve by long-pulse laser driven or other loading approaches. Additionally, experimental results also show that the free rear surface alternately experiences acceleration and deceleration, which indicates the spallation in the copper target. It is obvious that chirped pulse spectral interferometry is a reliable approach to studying ultrashort shock waves in metal films.