Plasmons in patterned graphene have attracted much interest because of possible applications in sensing, nanophotonics, and optoelectronics. We perform mid and far-infrared optical studies of electrically doped graphene nanoribbon arrays as a function of the filling factor and compare results with the unpatterned graphene. We demonstrate that an increase in both the filling factor of nanoribbon arrays and the free carrier concentration intensifies the plasmon-plasmon and plasmon-radiation interactions. As a result, the free-carrier dynamics manifested itself in the strong plasmon redshift and increased radiative damping compared to non-interacting models for the transverse magnetic polarization. Similarly, signatures of interactions are identified for plasmons in transverse electric polarization. The obtained experimental and theoretical results provide the basis for better understanding and controlling graphene-based structures’ spectral properties, thus facilitating applications’ development.