Carbon plays a crucial role in the search for extraterrestrial life and serves as an indicator for the habitability and the paleoatmospheric CO₂ reservoir on Mars. Previous exploration missions provided evidence of carbon on Mars with different chemical speciation using various instruments including laser-induced breakdown spectroscopy (LIBS). Quantitative determination with LIBS onboard Mars rovers is still precluded because of the important contribution of the atmospheric carbon in the LIBS plasma, in addition to matrix effects omnipresent for elemental determination with LIBS of geological materials. In this work, we performed a series of LIBS experiments in a simulated Martian atmosphere using samples prepared with a Martian soil simulant mixed with various carbonates and organic C-bearing materials. Convoluted influences on LIBS spectra due to the ambient gas and the different chemical speciation of carbon were observed for inorganic and organic C-bearing materials, which explains the unsatisfactory performance for a univariate regression model based on a carbon-related emission line. In particular, the influence of ambient gas was observed more important for inorganic carbon brought into the samples with carbonates. Multivariate models were then developed based on a back-propagation neural network (BPNN), for ensembles of samples with inorganic and organic carbons respectively, and then for the fusion of the two ensembles. The results showed respective limits of detection (LODs) of 0.247 wt%, 1.022 wt% and 0.873 wt%, and respective root mean square errors of prediction (RMSEPs) of 0.036 wt%, 0.133 wt%, and 0.062 wt% for the three collections of samples. Moreover, the model training process is investigated in detail in order to understand the way in which the most significant spectral features are selected, processed and mapped to the carbon concentrations of the samples by a neural network.