Urban flooding poses a growing challenge due to rapid urbanization and changing rainfall patterns, revealing the limitations of conventional drainage systems. This study introduces a nature-inspired, biomimetic solution, the Vein Logic drainage system, modeled on the adaptive branching structure of leaf veins, which enables efficient flow distribution through redundant and flexible pathways. Using a simulation of the Île de la Cité area along the Seine, the traditional drainage system initially transported water over 644.6 m before stopping at blocked channels, representing approximately 40% of the total route required to reach the target and illustrating the inability of conventional systems to maintain flow under obstruction. In contrast, the Vein Logic system dynamically rerouted around obstructions and successfully reached the target over a longer path of 1,590.6 m. Although the adaptive path is longer, it ensures continuous flow under blockage, demonstrating the trade-off between distance and reliability inherent in nature-inspired design. According to literature values reported over recent years, conventional urban drainage systems can experience 20–80% flow interruptions under partial blockages, further highlighting the need for adaptive, resilient networks. Practical implementation challenges are acknowledged, including spatial constraints and costs when retrofitting existing systems, and design complexity and the need for specialized expertise for new builds, emphasizing the considerations required for real-world application. These insights, together with the simulation results, demonstrate the potential of biomimicry and nature-inspired design to enhance urban drainage and flood management in contemporary cities, providing resilient infrastructure capable of maintaining functionality under adverse conditions. Moreover, the principles demonstrated here can be adapted to other urban contexts where conventional drainage systems face similar vulnerability, supporting broader applications of nature-inspired solutions.