We investigate the low-temperature electron transport through C 60 peapods, which are carbon nanotubes encapsulating C 60 fullerenes. We find that the temperature dependence of the Coulomb blockade oscillations in peapod quantum dots deviates from conventional Breit-Wigner behavior, showing signatures of the Franck-Condon blockade of conductance. This indicates the presence of a coupling between electronic states and vibrational excitations. Unlike for suspended empty nanotubes, these are not intrinsic vibrational modes of the tube but mechanical vibrations of the encapsulated fullerenes that affect the electronic transport. Fullerene peapods thus emerge as a new class of nanoelectromechanical systems.