  Current $\gamma$-ray telescopes suffer from a gap in sensitivity in the
energy range between 100keV and 100MeV, and no polarisation measurement has
ever been done on cosmic sources above 1MeV. Past and present e$^+$e$^-$ pair
telescopes are limited at lower energies by the multiple scattering of
electrons in passive tungsten converter plates. This results in low angular
resolution, and, consequently, a drop in sensitivity to point sources below
1GeV. The polarisation information, which is carried by the azimuthal angle of
the conversion plane, is lost for the same reasons.
  HARPO (Hermetic ARgon POlarimeter) is an R\&D program to characterise the
operation of a gaseous detector (a Time Projection Chamber or TPC) as a high
angular-resolution and sensitivity telescope and polarimeter for $\gamma$ rays
from cosmic sources. It represents a first step towards a future space
instrument in the MeV-GeV range.
  We built and characterised a 30cm cubic demonstrator [SPIE 91441M], and put
it in a polarised $\gamma$-ray beam at the NewSUBARU accelerator in Japan. Data
were taken at photon energies from 1.74MeV to 74MeV, and with different
polarisation configurations.
  We describe the experimental setup in beam. We then describe the software we
developed to reconstruct the photon conversion events, with special focus on
low energies. We also describe the thorough simulation of the detector used to
compare results. Finally we will present the performance of the detector as
extracted from this analysis and preliminary measurements of the polarisation
asymmetry.
  This beam-test qualification of a gas TPC prototype in a $\gamma$-ray beam
could open the way to high-performance $\gamma$-ray astronomy and polarimetry
in the MeV-GeV energy range in the near future.
