In the design of an extrinsic Fabry-Perot interferometer (EFPI) acoustic sensor, broadband response and high-sensitivity sensing are usually conflicting and need to be carefully balanced. Here, we present a novel, to the best of our knowledge, optical fiber acoustic sensor based on an ultra-thin diamond-like carbon (DLC) film, fabricated using the plasma-enhanced chemical vapor deposition method, and transferred by a surface-energy-assisted method. The sensor exhibits a broadband response ranging from 200 Hz to 100 kHz, maintains an average sensitivity of 457.3 mV/Pa within the range of 6 to 30 kHz, and can detect weak acoustic signals down to 3.23 µPa/Hz1/2@16.19 kHz. The combination of an ultra-thin DLC film with a relatively high Young's modulus and internal stresses results in a trade-off between high sensitivity and a broadband response. This performance demonstrates that our sensor is among the most advanced in the EFPI acoustic sensor family, with significant potential for applications such as photoacoustic spectroscopy, defect diagnosis, and bio-imaging.