The search of close (a<=5 au) giant planet(GP) companions with radial velocity(RV) around young stars and the estimate of their occurrence rates is important to constrain the migration timescales. Furthermore, this search will allow the giant planet occurrence rates to be computed at all separations via the combination with direct imaging techniques. 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 spots or pulsation in their RV time series. Specific analyses are necessary to characterize, and possibly correct for, this activity. Our aim is to search for planets around young nearby stars and to estimate the GP occurrence rates for periods up to 1000 days. We used the SOPHIE spectrograph to observe 63 A-M young (<400 Myr) stars. We used our SAFIR software to compute the RVs and other spectroscopic observables. We then combined this survey with the HARPS YNS survey to compute the companion occurrence rates on a total of 120 young A-M stars. We report one new trend compatible with a planetary companion on HD109647. We also report HD105693 and HD112097 as binaries, and we confirm the binarity of HD2454, HD13531, HD17250A, HD28945, HD39587, HD131156, HD 142229, HD186704A, and HD 195943. We constrained for the first time the orbital parameters of HD195943B. We refute the HD13507 single brown dwarf (BD) companion solution and propose a double BD companion solution. Based on our sample of 120 young stars, we obtain a GP occurrence rate of 1_{-0.3}^{+2.2}% for periods lower than 1000 days, and we obtain an upper limit on BD occurrence rateof 0.9_{-0.9}^{+2}% in the same period range. We report a possible lack of close (1<P<1000 days) GPs around young FK stars compared to their older counterparts, with a confidence level of 90%.
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