With the advent of Sustainable Finance Disclosure Regulation (SFDR), the question of the obsolescence of Socially Responsible Investment (SRI) labels in the fight against greenwashing has arisen in Europe. To address this question, this paper examines the portfolios of European funds, which hold the French SRI label at a stock level, in order to study their greenness. Our study relies on a clustering approach based on a set of widely used environmental performance metrics to differentiate European SRI labeled funds in terms of greenness. We document a decarbonization trend for SRI labeled funds that has accelerated since 2019. We also explain that the difference between dark and light green clusters of funds depends on their investment strategies. Dark green funds invest in a restricted number of equities while light green funds invest in a broader set of equities. Finally, we report significant discrepancies between SFDR categories and their expected degree of greenness, implying serious greenwashing concerns. Therefore, dividing the French SRI label into four grades fully compatible with the three EU’s SFDR categories allows to better capture the green heterogeneity of SRI labeled funds.