Context : The impact of the stellar mass on the giant planet properties is still to be fully understood .
Main-Sequence ( MS ) stars more massive than the Sun remain relatively unexplored in radial velocity ( RV ) surveys , due to their characteristics that hinder classical RV measurements .

Aims : Our aim is to characterize the close ( up to \sim 2 au ) giant planet ( GP ) and brown dwarf ( BD ) population around AF MS stars and compare this population to stars with different masses .

Methods : We used the S OPHIE spectrograph located on the 1.93m telescope at Observatoire de Haute-Provence to observe 125 northern , MS AF dwarfs .
We used our dedicated S AFIR software to compute the RV and other spectroscopic observables .
We characterized the detected substellar companions and computed the GP and BD occurrence rates combining the present S OPHIE survey and a similar H ARPS survey .

Results : We present new data on two known planetary systems around the F5-6V dwarfs HD 16232 and HD 113337 .
For the latter , we report an additional RV variation that might be induced by a second GP on a wider orbit .
We also report the detection of fifteen binaries or massive substellar companions with high-amplitude RV variations or long-term RV trends .
Based on 225 targets observed with S OPHIE and/or H ARPS , we constraint the BD frequency within 2-3 au around AF stars to be below 4 % ( 1 \sigma ) .
For Jupiter-mass GP within 2-3 au ( periods \leq 10 ^ { 3 } days ) , we found the occurrence rate to be 3.7 _ { -1 } ^ { +3 } % around AF stars with masses < 1.5 M _ { \sun } , and to be \leq 6 % ( 1 \sigma ) around AF stars with masses > 1.5 M _ { \sun } .
For periods smaller than 10 days , we find the GP occurrence rate to be below 3 or 4.5 % ( 1 \sigma ) , respectively .
Our results are compatible with the GP frequency reported around FGK dwarfs and are compatible with a possible increase of GP orbital periods with the stellar mass as predicted by formation models .

Conclusions :