This work aimed to produce bio-based poly(ethylene furanoate) (PEF) with a high molecular weight using 2,5-furan dicarboxylic acid (FDCA) or its derivative dimethyl 2,5-furan dicarboxylate (DMFD), targeting food packaging applications. The effect of monomer type, molar ratios, catalyst, polycondensation time, and temperature on synthesized samples’ intrinsic viscosities and color intensity was evaluated. It was found that FDCA is more effective than DMFD in producing PEF with higher molecular weight. A sum of complementary techniques was employed to study the structure–properties relationships of the prepared PEF samples, both in amorphous and semicrystalline states. The amorphous samples exhibited an increase in glass transition temperature of 82–87 °C, and annealed samples displayed a decrease in crystallinity with increasing intrinsic viscosity, as analyzed by differential scanning calorimetry and X-ray diffraction. Dielectric spectroscopy showed moderate local and segmental dynamics and high ionic conductivity for the 2,5-FDCA-based samples. The spherulite size and nuclei density of samples improved with increased melt crystallization and viscosity, respectively. The hydrophilicity and oxygen permeability of the samples were reduced with increased rigidity and molecular weight. The nanoindentation test showed that the hardness and elastic modulus of amorphous and annealed samples is higher at low viscosities due to high intermolecular interactions and degree of crystallinity.