Laser processing is a promising technique for graphene modification and patterning, with applications in the development of several electronic devices. In-situ Raman spectroscopy allows monitoring laser processing, providing information on numerous perturbations of the graphene lattice, such as disorder, strain, and doping, among others. This work focuses on the study of a graphene layer under prolonged irradiation with a femtosecond near-infrared laser at different average powers below the ablation threshold. The temporal evolution of the spectral parameters is analyzed, including the central position, width, and area of the main Raman bands attributed to graphene and silicon substrate, as well as the background signal. In addition, we present the correlation curves between most of these parameters. Our results show an initial instantaneous effect, linear with irradiation power, in which mainly p-type doping occurs. With prolonged fs-laser irradiation, the evolution of the spectral parameters can be divided into several intervals associated with different doping and strain stages. At each stage, the parameters present multiple time dependencies, nevertheless, several correlations between them are revealed. This work highlights the complexity of the evolution of the complete Raman spectrum of graphene and the relevance of a comprehensive multiparametric analysis.