Authors:Borgniet et alAbstract:Massive, Main-Sequence AF-type stars have so far remained unexplored in past radial velocity surveys, due to their small number of spectral lines and their high rotational velocities that prevent the classic RV computation method. Our aim was to search for giant planets around AF MS stars, to get first statistical information on their occurrence rate and to compare the results with evolved stars and lower-mass MS stars. We used the HARPS spectrograph located on the 3.6m telescope at ESO La Silla Observatory to observe 108 AF MS stars with B-V in the -0.04 to 0.58 range and masses in the range 1.1-3.6 Msun. We used our SAFIR software specifically developed to compute the radial velocities of these early-type stars. We report the new detection of a mpsini = 4.51 Mjup companion with a ~826-day period to the F6V dwarf HD111998. We present new data on the 2-planet system around the F6IV-V dwarf HD60532. We also report the detection of 14 binaries with long-term RV trends. 70% of our targets show detection limits between 0.1 and 10 Mjup in the 1 to 10^3-day range. We derive brown dwarf (13 < mpsini < 80 Mjup) occurrence rates in the 1 to 10^3-day range of 2+5−2% and 2.6+6.7−2.6% for stars with masses in the ranges 1.1-1.5 and 1.5-3 Msun, respectively. As for Jupiter-mass companions (1 < mpsini < 13 Mjup), we get occurrence rates in the 1 to 10^3-day range of 4+5.9−0.9% and 6.3+15.9−6.3% respectively for the same stellar mass ranges. When considering the same Jupiter-mass companions but periods in the 1 to 100-day range only, we get occurrence rates of 2+5.2−2% and 3.9+9.9−3.9%. Given the present error bars, these results do not show a significant difference with companion frequencies derived for solar-like stars.