Context. Transit spectroscopy is one of the most commonly used methods to characterize exoplanets' atmospheres. From the ground, these observations are very challenging due to the terrestrial atmosphere and its intrinsic variations, but high-spectral-resolution observations overcome this difficulty by resolving the spectral lines and taking advantage of the different Doppler velocities of the Earth, the host star, and the exoplanet. Aims: We analyze the transmission spectrum around the Na I doublet at 589 nm of the extrasolar planet WASP-69b, a hot Jupiter orbiting a K-type star with a period of 3.868 days, and compare the analysis to that of the well-known hot Jupiter HD 189733b. We also present the analysis of the Rossiter-McLaughlin (RM) effect for WASP-69b. Methods: We observed two transits of WASP-69b with the High Accuracy Radial velocity Planet Searcher (HARPS-North) spectrograph (R = 115 000) at the Telescopio Nazionale Galileo (TNG). We perform a telluric contamination subtraction based on the comparison between the observed spectra and a telluric water model. Then, the common steps of the differential spectroscopy are followed to extract the transmission spectrum. The method is tested with archival transit data of the extensively studied exoplanet HD 189733b, obtained with the HARPS-South spectrograph at ESO 3.6 m telescope, and then applied to WASP-69b data. Results: For HD 189733b, we spectrally resolve the Na I doublet and measure line contrasts of 0.72 ± 0.05% (D2) and 0.51 ± 0.05% (D1), and full width half maximum (FWHM) values of 0.64 ± 0.04 Å (D2) and 0.60 ± 0.06 Å (D1), in agreement with previously published results. For WASP-69b only the contrast of the D2 line can be measured (5.8 ± 0.3%). This corresponds to a detection at the 5σ-level of excess absorption of 0.5 ± 0.1% in a passband of 1.5 Å. A net blueshift of 0.04 Å is measured for HD 189733b and no shift is obtained for WASP-69b. By measuring the RM effect, we get an angular rotation of 0.24-0.01+0.02 rad/day and a sky-projected angle between the stellar rotation axis and the normal of orbit plane (λ) of 0.4-1.9+2.0° for WASP-69b. Similar results to those previously presented in the literature are obtained for the RM analysis of HD 189733b. Conclusions: Even if sodium features are clearly detected in the WASP-69b transmission spectrum, more transits are needed to fully characterize the line profiles and retrieve accurate atmospheric properties. The transmission spectra and the observed spectro-photometric light curves are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/608/A135