To foster responsible innovation, corporate governance lacks mechanisms that provide accountability for stakeholders on the companies’ innovation strategy, despite the radical uncertainty associated with grand societal challenges. A legal corporate form recently introduced in France, the société à mission, requires the creation of a specific governance body, a mission committee, which is expected to monitor the company’s execution of its purpose beyond profitability. This paper examines whether this new body introduces original governance mechanisms that are appropriate for innovative companies. It builds on participant observation in the mission committee of a French medium-sized company over seven years. This study opens a new avenue for responsible governance besides the reliance on deliberative capacities: a “generative governance” model which demands accountability on the firm’s efforts to explore knowledge gaps and alternative strategies that mobilize innovation capabilities to find improved solutions to current societal challenges.