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tokens: width of 0.26 Å for H and [OIII]. As an example, two performed fits are presented in Fig. 2 , including the central spaxel (with a ) and the lowest S/N spaxel () of the spatially binned MUSE observations. To quantify the impact of our fitting parameters on our results, we performed similar analyses but varying one parameter at a time. Firstly, we used additive polynomials of the 4th order, commonly used for fitting spectra on narrower, SAURON-like, wavelength range. Secondly, we masked all the potential emission lines from the galaxy, e.g. H, [OIII], H, [NII] and [SII]. Finally, we fitted the MUSE spectra on a restricted wavelength range (50005500 Å) that contains the Fe lines and the Mg triplet, which on their own strongly constrain the derived stellar kinematics. In all cases, we measured similar kinematics structures, with mean differences of only a few kilometers per second for the two first LOSVD moments, and , and mean differences of 0.001 to 0.02 for and . We should emphasise, however, that there are still clear systematic errors mostly regarding the third- and fourth-order moments and . The corresponding maps show some odd features, for example a clear offset of the level at the edges of the field (see Figs. 3 and 4 ). This is not surprising considering the original strong variation of the sky background (see Sect. 2.2 ), between exposures and also within the field of view of individual exposures (residual gradient). Assuming symmetric (odd or even) moment maps for and (with respect to the photometric minor axis), we estimate these systematic errors to 0.02 for and 0.05 for . 3.2. Stellar kinematics results Fig. 4 One-dimensional curve of the first four line-of-sight velocity distribution (LOSVD) moments: a) stellar radial velocity, V; b) stellar velocity dispersion, ; c) third-order Gauss-Hermite moment, ; d) fourth-order Gauss-Hermite moment, . The points were extracted from the two-dimensional maps of the respective quantities (see Fig. 3 ), by taking the light-weighted mean value within a 2 wide slit, aligned with the major axis (orange points), and offset by +8 (green points) and +20 (blue points) along the minor axis. We present in Fig. 3 the stellar kinematics maps of NGC 3115, obtained as described in Sect. 3.1 from our MUSE reduced cube. The mean radial stellar velocity map (Fig. 3 , panel a) exhibits a fast-rotating structure, similar to a thin disc, embedded in a slower spheroidal component, but still rotating fairly rapidly. The thin disc structure has an apparent vertical extent (with respect to the major axis) widening from a few arcseconds near the centre to (i.e. 930 pc) at about two effective radii (i.e. 70 or 3.4 kpc) where it becomes blended with the spheroidal part of the galaxy. The thinness of the kinematic disc also confirms that NGC 3115 is viewed almost edge-on. Along the major axis, the mean radial stellar velocity curve exhibits a double maximum (see Fig. 4 , panel a) with a first steep rise to 150 km s