Green finance is an economic form formed by the organic combination of finance and environmental awareness, and the long-term development of a low-carbon economy needs to be strongly supported by green finance. Based on the generalized regression neural network model, this paper measures the level of green finance development in a low-carbon economy by constructing a green finance evaluation system. The evaluation system for enterprise adaptability level under green finance is constructed from three dimensions: enterprise green development ability, enterprise green innovation ability, and enterprise green management ability. The entropy weight method is used to empower the indicators in the rating system, and the set-pair theory is used to portray the data of the empowered indicators, while the Markov chain combined with the set-pair linkage is introduced to portray the dynamic trend of the development of enterprise adaptability level. The generalized regression neural network model’s prediction accuracy for green finance development in Guangdong Province is above 85% after the study. Year-on-year, the level of green finance development in Guangdong Province increased by around 57.78%, creating a significant growth trend in the context of a low-carbon economy between 2010 and 2017. The level of business adaptability also leaps from “poor” to “excellent”, with the linkage value changing from −0.8574 in 2018 to 0.8031 in 2022. This paper’s research provides the perfect data support for choosing a green financial innovation path only in a low carbon economy.