Distributed Acoustic Sensing (DAS) is a nascent technology that facilitates the measurement of vibrations along fibre-optic telecommunication cables, which has numerous novel applications in many domains of science and engineering. In the present study, we use DAS to analyse traffic along a fibre-optic cable deployed along a major road in Nice, France. For the objective of estimating the speed of individual vehicles, we propose a MUSIC beamforming algorithm, which exhibits superior performance when applied to data that has been deconvolved with a Deep Learning model. The accuracy of the speed estimation is in the range of 0.14-0.25 km/h , which is at least one order of magnitude better than conventional methods. DAS therefore has great potential in urban traffic analysis applications.