Hybrid catalysis, which combines chemo‐ and biocatalytic benefits, is an efficient way to address green chemistry principles. 5‐Hydroxymethylfurfural (HMF) is a versatile building block in numerous industrial applications. To date, few studies have described the production of its amine derivatives and their polymers. Finding a good methodology to directly transform HMF to 5‐aminomethyl‐2‐furancarboxylic acid (AMFC) therefore represents an important challenge. After selecting the best oxidation catalyst for HMF conversion to 5‐aldehyde‐2‐furancarboxylic acid and immobilizing a transaminase onto a solid carrier, we implemented the first one‐pot/two‐steps hybrid catalytic process to produce AMFC (77 % yield); this is the most efficient AMFC catalytic production method from HMF reported to date. This process also produced 2,5‐furandicarboxylic acid (21 % yield) as a major secondary product that can be applied to polymer syntheses such as polyethylene furanoate. Herein, we report a novel way to access new biosourced polymers based on HMF oxidized and aminated derivatives.