[en] Laser Plasma Acceleration (LPA) [1] is an emerging concept enabling to generate electron beams with high energy, high peak current and small transverse emittance within a very short distance. The use of LPA can be applied to the Free Electron Laser (FEL) [2] case in order to investigate whether it is suitable for the light amplification in the undulator. However, capturing and guiding of such beams to the undulator is very challenging, because of the large divergence and high energy spread of the electron beams at the plasma exit, leading to large chromatic emittances. A specific beam manipulation scheme was recently proposed for the COXINEL (Coherent X-ray source inferred from electrons accelerated by laser) setup, which makes an advantage from the intrinsically large chromatic emittance of such beams [3]. The electron beam transport is studied using two simulation codes: a SOLEIL in-house one and ASTRA [4]. The influence of the collective effects on the electron beam performance is also examined.