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We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e.contractivity for a modified $L^2$ norm, implies quantitative deviation boundsfor additive functionals of the associated Markov process and exponentialintegrability of the hitting time of sets with positive measure. Moreover, inthe case of diffusion processes and under a strong hypoellipticity assumption,we prove that $L^2$ hypocoercivity implies the existence of a Lyapunov functionfor the generator. An english translation of the original article in french isprovided.    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 desin\'egalit\'es de concentration quantitatives et l'int\'egrabilit\'eexponentielle des temps d'atteinte des ensembles de mesure positive. D'autrepart, 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 deLyapunov pour le g\'en\'erateur associ\'e. Une traduction en anglais estdisponible.

Hypocoercivit\'e $L^2$, in\'egalit\'e de concentration, temps d'atteinte et fonctions de Lyapunov