  (Abridged) Aims: Systematic surveys to search for exoplanets have been mostly
dedicated to solar-type stars sofar. We developed in 2004 a method to extend
such searches to earlier A-F type dwarfs and started spectroscopic surveys to
search for planets and quantify the detection limit achievable when taking into
account the stars properties and their actual levels of intrinsic variations.
We give here the first results of our southern survey with HARPS.
  Results: 1) 64% of the 170 stars with enough data points are found to be
variable. 20 are found to be binaries or candidate binaries (with stars or
brown dwarfs). More than 80% or the latest type stars (once binaries are
removed) are intrinsically variable at a 2 m/s precision level. Stars with
earlier spectral type (B-V <= 0.2) are either variable or associated to levels
of uncertainties comparable to the RV rms observed on variable stars of same
B-V. 2) We have detected one long-period planetary system around an F6IV-V
star. 3) We have quantified the jitter due to stellar activity and we show that
taking into account this jitter in addition to the stellar parameters, it is
still possible to detect planets with HARPS with periods of 3 days (resp. 10
days and 100 days) on 91% (resp. 83%, 61%) of them. We show that even the
earliest spectral type stars are accessible to this type of search, provided
they have a low vsini and low levels of activity. 4) Taking into account the
present data, we compute the actually achieved detection limits for 107 targets
and discuss the limits as a function of B-V. Given the data at hand, our survey
is sensitive to short-period (few days) planets and to longer ones (100 days)
at a lower extent (latest type stars). We derive first constrains on the
presence of planets around A-F stars for these ranges of periods.
