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Current $\gamma$-ray telescopes suffer from a gap in sensitivity in theenergy range between 100keV and 100MeV, and no polarisation measurement hasever been done on cosmic sources above 1MeV. Past and present e$^+$e$^-$ pairtelescopes are limited at lower energies by the multiple scattering ofelectrons in passive tungsten converter plates. This results in low angularresolution, and, consequently, a drop in sensitivity to point sources below1GeV. The polarisation information, which is carried by the azimuthal angle ofthe conversion plane, is lost for the same reasons.  HARPO (Hermetic ARgon POlarimeter) is an R\&D program to characterise theoperation of a gaseous detector (a Time Projection Chamber or TPC) as a highangular-resolution and sensitivity telescope and polarimeter for $\gamma$ raysfrom cosmic sources. It represents a first step towards a future spaceinstrument in the MeV-GeV range.  We built and characterised a 30cm cubic demonstrator [SPIE 91441M], and putit in a polarised $\gamma$-ray beam at the NewSUBARU accelerator in Japan. Datawere taken at photon energies from 1.74MeV to 74MeV, and with differentpolarisation configurations.  We describe the experimental setup in beam. We then describe the software wedeveloped to reconstruct the photon conversion events, with special focus onlow energies. We also describe the thorough simulation of the detector used tocompare results. Finally we will present the performance of the detector asextracted from this analysis and preliminary measurements of the polarisationasymmetry.  This beam-test qualification of a gas TPC prototype in a $\gamma$-ray beamcould open the way to high-performance $\gamma$-ray astronomy and polarimetryin the MeV-GeV energy range in the near future.

First measurement of polarisation asymmetry of a gamma-ray beam between 1.74 to 74 MeV with the HARPO TPC