What is the name of this injured species?
Well, after a lot of research, I hardy believe that it is a Rhizotrogus aestivus. First of all, the size (2-3cm) you mentioned fits exactly. Secondly, the colour matches fair enough. Finally the antennas and the body shape, may not be seen very well in the picture but I assume that they match. The only thing that I am not sure is the "laziness" of that insect, beacause they are only lazy or clumsy and not active, only when they are about to die.

For more informations check here: https://inpn.mnhn.fr/espece/cd_nom/10907?lg=en