Crop residues are acknowledged as a key biomass resource to feed tomorrow's sustainable bioeconomy. Yet, the quantification of these residues at large geographical scales is primarily reliant upon generic statistical estimations based on empirical functions linking the residues production to the primary crop yield. These useful yet unquestioned functions are developed either using direct evidence from experimental results or literature. In the present study, analytical evidence is presented to demonstrate that these methods generate imprecise and likely inaccurate estimates of the actual biophysical crop residue potential. In this endeavor, we applied five of the most used functions to a national case study. France was selected, being the country with the largest agricultural output in Europe. Our spatially-explicit assessment of crop residues production was performed with a spatial resolution corresponding to the level of an administrative department (96 departments in total), also the finest division of the European Union's hierarchical system of nomenclature for territorial units (NUTS), and included 16 different crop residues. The theoretical potential of crop residues for France was found to vary from 987 PJ y(-1)- to 1369 PJ y(-1), using different estimation functions. The difference observed is more than the entire annual electricity consumption of Belgium, Latvia, and Estonia combined. Perturbation analyses revealed that some of the functions are overly sensitive to fluctuation in primary crop yield, while analytical techniques such as the null hypothesis statistical test indicated that the crop residues estimates stemming from all functions were all significantly different from one another.