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              <p>We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e. contractivity for a modified $L^2$ norm, implies quantitative deviation bounds for additive functionals of the associated Markov process and exponential integrability of the hitting time of sets with positive measure. Moreover, in the case of diffusion processes and under a strong hypoellipticity assumption, we prove that $L^2$ hypocoercivity implies the existence of a Lyapunov function for the generator. An english translation of the original article in french is provided. ----- On montre que, pour un semi-groupe de Markov, l'hypocoercivit\'e $L^2$ -- c'est-\`a-dire la contractivit\'e d'une norme $L^2$ modifi\'ee -- implique des in\'egalit\'es de concentration quantitatives et l'int\'egrabilit\'e exponentielle des temps d'atteinte des ensembles de mesure positive. D'autre part, pour les diffusions et sous une hypoth\`ese forte d'hypoellipticit\'e, on \'etablit que l'hypocoercivit\'e $L^2$ implique l'existence d'une fonction de Lyapunov pour le g\'en\'erateur associ\'e. Une traduction en anglais est disponible.</p>
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