We investigate the fluctuations of linear spectral statistics of a Wigner matrix \(W_N\) deformed by a deterministic diagonal perturbation \(D_N\) , around a deterministic equivalent which can be expressed in terms of the free convolution between a semicircular distribution and the empirical spectral measure of \(D_N\) . We obtain Gaussian fluctuations for test functions in \(\mathcal {C}_c^7(\mathbb {R})\) ( \(\mathcal {C}_c^2(\mathbb {R})\) for fluctuations around the mean). Furthermore, we provide as a tool a general method inspired from Shcherbina and Johansson to extend the convergence of the bias if there is a bound on the bias of the trace of the resolvent of a random matrix. Finally, we state and prove an asymptotic infinitesimal freeness result for independent GUE matrices together with a family of deterministic matrices, generalizing the main result from Shlyakhtenko (Indiana Univ Math J 67(2):971–991, 2018).