Innovation represents one of the most important drivers in the business context. Drawing upon the research on corporate social responsibility (CSR), shared value, and innovation, this paper aims to analyze the relationship between Environmental, Social, and Governance (ESG, a form of CSR) sustainability policies and corporate financial performance (CFP) by investigating the mediating role of Innovation (i.e., investment in research and development, R&D). Our sample comprises 148 European companies belonging to the Euro Stoxx index in the period 2009–2014. For high‐innovation companies (HICs), we find positive relationships between some Social (S) issues and CFP and weaker linkages between Environmental (E) indicators and CFP. In contrast, Governance (G) issues (i.e., issues related to board structure and board function) negatively influence CFP. In contrast, for medium‐innovation companies (MICs), these relationships are absent and low‐innovation companies (LICs) show negative relationships. Adopting reporting frameworks or guidelines affects CFP only in HIC. We introduce an original interpretative model, which identifies innovation (R&D) as the main driver in corporate sustainability, particularly in light of Social issues related to the production of a good or service. In terms of managerial implications, we identify three key factors for effectively embedding ESG in organizations' policies: investment in product innovation, compliance with environmental regulations, and corporate choices on brands and channels of external communication.