Friction reduction at tribological interfaces remains a long-standing topic of both academic and industrial significance. Copper substrates are widely employed in various applications; however, their relatively low hardness necessitates effective strategies for friction and wear protection. In this study, a synergistic approach combining electrodeposited Ni–Co coatings and picosecond laser surface texturing was developed. An orthogonal experiment design was conducted to optimize the laser processing parameters using micro-scale equilateral triangular textures, ensuring sharp edges and minimal thermal damage. The effects of CoSO₄·7H₂O concentration on surface morphology, phase composition, microhardness, and tribological performance were systematically investigated. The results showed that optimal Co incorporation significantly refined the grains and improved both hardness and wear resistance. Furthermore, micro-textures reduced friction and enhanced lubrication, producing a clear synergistic effect. At the optimal CoSO₄·7H₂O concentration of 150   g/L, the Vickers hardness reached 282.5 HV, the crystallite size of the Ni–Co coating decreased to 20.03   nm, and the steady-state coefficient of friction (COF) was reduced to 0.0150, corresponding to a reduction of approximately 77.9% compared with the untreated substrate. Mechanistic analysis indicates that the Ni–Co coating contributes grain refinement and solid-solution strengthening, whereas the triangular micro-textures trap wear debris and enhance the load-bearing capacity of the lubricant film. The combined effects of hardness enhancement and lubrication improvement effectively mitigate friction and wear. These findings provide a practical strategy for fabricating low-friction and wear-resistant coatings on copper substrates for advanced tribological applications.