Nanocomposites based on bio-based Poly(ethylene 2,5-furandicarboxylate), PEF, and different nanoclays (either sepiolite or montmorillonite, both organically modified) were prepared by melt extrusion and compression molding. Firstly, the impact of processing at high temperatures on PEF molecular weight is evaluated and correlated to the presence of the different clays used in the nanocomposite. Then, the melt- and the solid-state properties of PEF nanocomposites are characterized by using different analytical techniques (rheological tests, TGA, DSC, DMA). It is shown how some clay features such as the clay organo-modification may affect the polymer behavior.