Context. Young nearby stars are good candidates in the search for planets with both radial velocity (RV) and direct imaging techniques. This, in turn, allows for the computation of the giant planet occurrence rates at all separations. The RV search around young stars is a challenge as they are generally faster rotators than older stars of similar spectral types and they exhibit signatures of magnetic activity (spots) or pulsation in their RV time series. Specific analyses are necessary to characterize, and possibly correct for, this activity. Aims. Our aim is to search for planets around young nearby stars and to estimate the giant planet (GP) occurrence rates for periods up to 1000 days. Methods. We used the HARPS spectrograph on the 3.6 m telescope at La Silla Observatory to observe 89 A−M young (<600 Myr) stars. We used our SAFIR (Spectroscopic data via Analysis of the Fourier Interspectrum Radial velocities) software to compute the RV and other spectroscopic observables. Then, we computed the companion occurrence rates on this sample. Results. We confirm the binary nature of HD 177171, HD 181321 and HD 186704. We report the detection of a close low mass stellar companion for HIP 36985. No planetary companion was detected. We obtain upper limits on the GP (<13 M_Jup) and BD (∈ [13;80] M_Jup) occurrence rates based on 83 young stars for periods less than 1000 days, which are set, 2₋₂⁺³ and 1₋₁⁺³%.