In this paper, we first report the recent achievement of a mid-infrared supercontinuum fiber laser source in our laboratory. Using fluoride fibers, we have generated a wavelength supercontinuum covering the whole 2-3.5μm range, and delivering a power spectral density of 0.3 mW/nm on a large spectral range. Experimental results are presented. This source can open opportunities for broadband remote sensing of multiple gas species in the atmosphere, especially above 3 μm, where numerous organic compounds have strong absorption signatures. Therefore, we consider a simple Supercontinuum Laser Absorption Spectroscopy (SLAS) experiment, and we develop a numerical case study above 3 μm, involving a multi-component gas mixture. We first describe a method for modelling noisy spectroscopic signals. Then we consider the inverse problem, and attempt to perform identification and quantitative estimation of the gas mixture. After showing the inapplicability of a direct multi-linear regression, we focus on processing methods that use complexity penalization principles, and show that they can address efficiently the identification/estimation problem. Among various penalization criteria, those based on Minimum Description Length (MDL) approaches are shown to perform particularly well. Finally, we apply these methods to preliminary experimental spectroscopic signals obtained with supercontinuum sources in our laboratory.