Context. The HEARTS survey aims to probe the upper layers of the atmosphere by detecting resolved sodium doublet lines, a tracer of the temperature gradient, and atmospheric winds. KELT-10b, one of the targets of HEARTS, is a hot-inflated Jupiter with 1.4 RJup and 0.7 MJup. Recently, there was a report of sodium absorption in the atmosphere of KELT-10b (0.66% ± 0.09% (D2) and 0.43% ± 0.09% (D1); VLT/UVES data from single transit). Aims. We searched for potential atmospheric species in KELT-10b, focusing on sodium doublet lines (Na I; 589 nm) and the Balmer alpha line (H α; 656 nm) in the transmission spectrum. Furthermore, we measured the planet-orbital alignment with the spin of its host star. Methods. We used the Rossiter–McLaughlin Revolutions technique to analyze the local stellar lines occulted by the planet during its transit. We used the standard transmission spectroscopy method to probe the planetary atmosphere, including the correction for telluric lines and the Rossiter–McLaughlin effect on the spectra. We analyzed two new light curves jointly with the public photometry observations. Results. We do not detect signals in the Na I and H α lines within the uncertainty of our measurements. We derive the 3σ upper limit of excess absorption due to the planetary atmosphere corresponding to equivalent height Rp to 1.8Rp (Na I) and 1.9Rp (H α). The analysis of the Rossiter–McLaughlin effect yields the sky-projected spin-orbit angle of the system λ = −5.2 ± 3.4◦ and the stellar projected equatorial velocity veq sin i⋆ = 2.58 ± 0.12 km s−1. Photometry results are compatible within 1σ with previous studies. Conclusions. We found no evidence of Na I and H α, within the precision of our data, in the atmosphere of KELT-10b. Our detection limits allow us to rule out the presence of neutral sodium or excited hydrogen in an escaping extended atmosphere around KELT-10b. We cannot confirm the previous detection of Na I at lower altitudes with VLT/UVES. We note, however, that the Rossiter–McLaughlin effect impacts the transmission spectrum on a smaller scale than the previous detection with UVES. Analysis of the planet-occulted stellar lines shows the sky-projected alignment of the system, which is likely truly aligned due to tidal interactions of the planet with its cool (Teff < 6250 K) host star.