Underwater fiber optic cables commonly traverse a variety of seafloor conditions, which leads to an uneven mechanical coupling between the cable and the ocean bottom. On rough seafloor bathymetry, some cable portions might be suspended and thus susceptible to Vortex-Induced Vibrations (VIV) driven by deep ocean currents. Here, we examine the potential of Distributed Acoustic Sensing (DAS) to monitor deep-sea currents along suspended sections of underwater telecom fiber optic cables undergoing VIV. Oscillations of a seafloor fiber optic cable located in southern France are recorded by DAS along cable sections presumably hanging. Their characteristic frequencies are lower than 1 Hz, at different ocean depths, and have an amplitude-dependency consistent with the driving mechanism being VIV. Based on a theoretical proportionality between current speed and VIV frequencies, we derive ocean current speed time series at 2390 m depth from the vortex shedding frequencies recorded by DAS. The DAS-derived current speed time series is in agreement with recordings by a current meter located 3.75 km away from the hanging cable section (similar dominant period, high correlation after time shift). The DAS-derived current speed time series displays features, such as characteristic periods and spectral decay, associated with the generation of internal gravity waves and weak oceanic turbulence in the Mediterranean Sea. The results demonstrate the potential of DAS along hanging segments of fiber optic cables to monitor a wide range of oceanography processes, at depths barely studied with current instrumentation.