A rapid and effective technique has been develped for the fabrication of sensor-active copper-based materials on the surface of such flexible polymers as terephthalate, polyethylene naphthalate, and polyimide using the method of laser surface modification. For this purpose, we optimized the polymer surface activation parameters using laser sources with a picosecond pulse duration for subsequent selective metallization within the activated region. Furthermore, the fabricated copper structures were modified with gold nanostructures and by electrochemical passivation to produce copper–gold and oxide-containing copper species, respectively. As a result, in comparison with pure copper electrodes, these composite materials exhibit much better electrocatalytic performance concerning the non-enzymatic identification of biologically important disease markers such as glucose, hydrogen peroxide, and dopamine. Graphical abstract: [Figure not available: see fulltext.].