The ultra-faint dwarf galaxies (UFDs) are some of the oldest and most metal-poor environments in the Local Group. In particular, they are predicted to host the first stars (only H and He) that lit up in our Universe. No metal-free stars have been found to date, but their chemical products can be observed on the surfaces of the ancient second-generation stars such as the carbon-enhanced metal-poor stars (CEMP-no, [C/Fe] > +0.7). However, in each UFD there are only a few stars bright enough for spectroscopic follow-up; therefore, it is crucial to study as many of these systems as possible. In this work, we followed up on stars belonging to two recently discovered UFDs: Grus II and Tucana IV. The spectra analyzed were obtained with the multi-object spectrograph FLAMES-Giraffe at the Very Large Telescope (VLT). This includes spectra in two wavelength ranges: red spectra around the Ca II triplet (8498 Å, 8542 Å, 8662 Å) used to derive radial velocity and [Fe/H], and blue spectra covering the CH band at ~4300Å. In total, we analyzed 21 spectra of member candidates for Grus II and 17 for Tucana IV, including both red giant branch (RGB) and horizontal branch (HB) stars. We identified 13 members in Grus II (eight of which are RGB stars) and seven members in Tucana IV (three of which are RGB stars). Among the RGB stars in Grus II, we found three CEMP-no stars at [Fe/H] ≍ -3 and [C/Fe] > +1 and two CEMP-no stars at a slightly higher [Fe/H] and [C/Fe] > +0.7. In Tucana IV, we found one CEMP-no star ([Fe/H] = -2.75 and [C/Fe] = +0.83). This project, along with future investigations of CEMP stars in UFDs, allows us to study the impact of the first stars in these ancient and primitive systems and consequently the first chemical enrichment that occurred in the Universe.