Context : Massive , Main-Sequence AF-type stars have so far remained unexplored in past RV surveys , due to their small number of spectral lines and their high rotational velocities that prevent the classic RV computation method . Aims : Our aim is to search for giant planets ( GP ) around massive AF Main-Sequence stars , to get first statistical information on their occurrence rate and to compare the results with evolved stars and lower-mass Main-Sequence stars . Methods : We used the H ARPS spectrograph located on the 3.6m telescope at ESO La Silla Observatory to observe 108 AF Main-Sequence stars with B - V in the range - 0.04 to 0.58 and masses in the range 1.1-3.6 M _ { \sun } . We used our SAFIR software developed to compute the RV and other spectroscopic observables of these early-type stars . We characterized the detected companions as well as the intrinsic stellar variability . We computed the detection limits and used them as well as the detected companions to derive the first estimate of the close-in brown dwarf and giant planet frequencies around AF stars . Results : Giant planets : We report the new detection of a m _ { p } \sin { i } = 4.51 M _ { Jup } planetary companion with a \sim 826-day period to the F6V dwarf HD 111998 . We also present new data on the 2-planet system around the F6IV-V dwarf HD 60532 . Spectroscopic binaries : We also report the detections of 14 binaries with long-term RV trends and/or high-amplitude RV variations combined to a flat RV-bisector span diagram . We constrain the minimal masses and sma of these companions and check that these constrains are compatible with the stellar companions previously detected by direct imaging or astrometry for six of these targets . Detection limits : We get detection limits deep into the planetary domain with 70 % of our targets showing detection limits between 0.1 and 10 M _ { Jup } at all orbital periods in the 1 to 10 ^ { 3 } -day range . Statistics : We derive brown dwarf ( 13 \leq m _ { p } \sin { i } \leq 80 M _ { Jup } ) occurrence rates in the 1 to 10 ^ { 3 } -day period range of 2 _ { -2 } ^ { +5 } % and 2.6 _ { -2.6 } ^ { +6.7 } % for stars with M _ { \star } in the ranges 1.1-1.5 and 1.5-3 M _ { \sun } , respectively . As for Jupiter-mass companions ( 1 \leq m _ { p } \sin { i } \leq 13 M _ { Jup } ) , we get occurrence rates in the 1 to 10 ^ { 3 } -day period range of 4 _ { -0.9 } ^ { +5.9 } % and 6.3 _ { -6.3 } ^ { +15.9 } % respectively for the same M _ { \star } ranges . When considering the same Jupiter-mass companions but periods in the 1 to 100-day range only , we get occurrence rates of 2 _ { -2 } ^ { +5.2 } % and 3.9 _ { -3.9 } ^ { +9.9 } % . Given the present error bars , these results do not show a significant difference with companion frequencies derived in the same domains for solar-like Main-Sequence stars . Conclusions :