This paper develops a two-way director-firm fixed effect model to study the relationship between independent directors' individual heterogeneity and firm operating performance, using French data. This strategy allows considering and differentiating in a unified empirical framework mechanisms related to board functioning and to director selection. We first show that the independence status, netted out unobservable individual heterogeneity, is negatively related to performance. This result suggests that independent board members experience an informational gap compared to other affiliated members. However, we show that industry-specific expertise as well as informal connections inside the boardroom may help to bridge this gap. Finally, we provide evidence that independent directors have higher intrinsic ability as compared to affiliated board members, consistent with a reputation-based selection process.