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PurposeThis study aims to investigate whether threshold effects exist in the relationship between board gender diversity and firm performance.Design/methodology/approachThis study applies the panel smooth threshold regression model (PSTR) to a sample of 284 non-financial French firms listed on Euronext Paris over the period 2009–2017. Firm performance proxies are Tobin's Q and return on assets (ROA). The board gender diversity is measured by the percentage of women participation in board.FindingsThreshold effects in the relationships between board gender diversity and firm performance measures are found. For Tobin's Q, the model has one threshold at the 34.17% of women directors' appointment on boards. Similarly, for ROA, the model has one threshold at the 38.28% of women presence in the board. The results show that above the estimated threshold, women directorship has a positive impact on firm performance. However, below the threshold, there is a neutral relationship. The findings support the critical mass view that a minimum of one third women representation in board is compulsory to achieve the desired effect of gender diversity.Practical implicationsThis study's finding provides useful insights to managers, investors and policymakers. Managers and investors can identify the adequate board gender diversity levels that enhance firm performance. Policymakers are divided on whether mandatory or voluntary board gender quota should be adopted. This study suggests that a quota of one third can be used in policy implementation.Originality/valueUnlike prior studies that consider the relationship between firm performance and board gender diversity as linear, to the best of the authors' knowledge, this study is the first to investigate the threshold effects in this relationship using a new econometric approach.