Poly(ethylene 2,5-furandicarboxylate) (PEF) nanocomposites reinforced with various content of graphene nanoplatelets (GNPs) were synthesized in situ in this work. PEF is a widely known biobased polyester with promising physical properties and is considered as the sustainable counterpart of PET. Despite its exceptional gas barrier and mechanical properties, PEF presents with a low crystallization rate. In this context, a small number of GNPs were incorporated into the material to facilitate the nucleation and overall crystallization of the matrix. Kinetic analysis of both the cold and melt crystallization processes of the prepared materials was achieved by means of differential scanning calorimetry (DSC). The prepared materials’ isothermal crystallization from the glass and melt states was studied using the Avrami and Hoffman–Lauritzen theories. The Dobreva method was applied for the non-isothermal DSC measurements to calculate the nucleation efficiency of the GNPs on the PEF matrix. Furthermore, Vyazovkin’s isoconversional method was employed to estimate the effective activation energy values of the amorphous materials’ glass transition. Finally, the nanomechanical properties of the amorphous and semicrystalline PEF materials were evaluated via nanoindentation measurements. It is shown that the GNPs facilitate the crystallization process through heterogeneous nucleation and, at the same time, improve the nanomechanical behavior of PEF, with the semicrystalline samples presenting with the larger enhancements.