In this manuscript, we introduce a flexible methodology for approximating the systematic component, the single-index vector, and the regression operator in the context of a functional predictor and a scalar response. Following the Fisher-scoring algorithm and the principle of projection pursuit regression, we derive an additive decomposition that exploits the most predictive direction, the most predictive additive component of the functional predictor variable and the single-index component to explain the scalar response. On the one hand, this approach allows us to avoid the well-known problem of the curse of dimensionality in the nonparametric case with the notion of single-index and the projection pursuit regression in the functional case. On the other hand, it can be used as an exploratory tool for the analysis of a multivariate and functional random variable belonging to a separable Hilbert space \( \mathcal{H} \) . The terms of this decomposition are estimated with an iterative Fisher scoring procedure that uses the Quasi-Likelihood function and an approximation of the nonparametric function by normalized B-splines. The good behavior of our procedure is illustrated from a theoretical and practical points of view. Asymptotic results indicate that the nonparametric function, the single index coefficient and the terms of the additive decomposition can be estimated without suffering from the curse of dimensionality.