Context. There are no strong constraints placed thus far on the amplitude of internal gravity waves (IGWs) that are stochastically excited in the radiative interiors of solar-type stars. Late F-type stars have relatively thin convective envelopes with fast convective flows and tend to be fast rotators compared to solar-type stars of later spectral types. These two elements are expected to directly impact the IGW excitation rates and properties. Aims. We want to estimate the amplitude of stochastically excited gravity modes (g-modes) in F-type stars for different rotational regimes. Methods. We used the ASH code to perform 3D simulations of deep-shell models of 1.3 M⊙ F-type solar-type stars, including the radiative interior and the shallow convective envelope. Results. We found different differential rotation regimes in the convective zone, depending on the rotation rate we imposed on the stellar models. We find that the convective structures and the overshoot properties are affected by rotation. The IGWs are excited by interface interactions between convective plumes and the top of the radiative interior. We were able to characterise the IGWs and g-mode properties in the radiative interior, and we compared these properties using the computation from the 1D oscillation code GYRE. The amplitude of low-frequency modes is significantly higher in fast-rotating models and the evolution of the period spacing of consecutive modes exhibits evidence of a behaviour that is modified by the influence of the Coriolis force. For our fastest rotating model, we were able to detect the intermediate degree g-mode signature near the top of the simulation domain. Nevertheless, the predicted luminosity perturbations from individual modes still remain at small amplitudes. Conclusions. We obtained mode amplitudes that are several orders of magnitude higher than those of prior 3D simulations of solar models. Our simulations suggest that g-mode signatures could be detectable in late F-type stars, which are the hottest main-sequence solar-type pulsating stars. We therefore emphasise that they constitute object of primary importance for improving our understanding of internal stellar dynamics.