Under the guidance of “carbon peaking and carbon neutrality”, “ecological priority” and “green development” have become the popular consensus, and the financial regulatory level continuously guides financial institutions to increase investment in green and low carbon projects. In the field of green financial supervision in China, due to imperfect systems and poor adaptability, financial risks are often difficult to control within a reasonable range, which has had a significant impact on financial supervision and management. This article aimed to optimize the green financial regulatory information system under the carbon peaking and carbon neutrality goals. Firstly, this article analyzed the concept and background of green finance regulation; then, an investigation was conducted on the construction of the green finance service information system, and a green finance information system supervision plan was established. Finally, data collection and analysis were conducted, and the supervision of the green finance information system was carried out using a standard genetic algorithm based on a fuzzy evaluation matrix. This article used a genetic algorithm to optimize the green financial regulatory information system, and selected 500 people to evaluate the use of the system before and after the optimization. The proportion of very satisfied people increased from 11.2% to 19.2%; the proportion of satisfied people increased from 17.2% to 37.6%; the proportion of people who were very dissatisfied decreased from 14.4% to 3.6%. The experiment in this article showed that the optimized system could operate more stably, and the process was more reasonable. The statistical analysis ability was significantly enhanced, and the functions were more comprehensive. This suggests that the system could better regulate the development of green finance.