A study on cosmic muons has been performed for the two identical near and far neutrino detectors of the Double Chooz experiment, placed at $sim$120 and $sim$300 m.w.e. underground respectively, including the corresponding simulations using the MUSIC simulation package. This characterization has allowed to measure the muon flux reaching both detectors to be (3.64 $pm$ 0.04) $times$ 10$^{-4}$ cm$^{-2}$s$^{-1}$ for the near detector and (7.00 $pm$ 0.05) $times$ 10$^{-5}$ cm$^{-2}$s$^{-1}$ for the far one. The seasonal modulation of the signal has also been studied observing a positive correlation with the atmospheric temperature, leading to an effective temperature coefficient of $alpha_{T}$ = 0.212 $pm$ 0.024 and 0.355 $pm$ 0.019 for the near and far detectors respectively. These measurements, in good agreement with expectations based on theoretical models, represent one of the first measurements of this coefficient in shallow depth installations.
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