We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission . We simulate a three-prong SN survey : a z < 0.35 nearby sample ( 8000 SNe ) , a 0.2 < z < 0.95 intermediate sample ( 8800 SNe ) , and a 0.75 < z < 1.55 high- z sample ( 1700 SNe ) . The nearby and intermediate surveys are assumed to be conducted from the ground , while the high-z is a joint ground- and space-based survey . This latter survey , the ” Dark Energy Supernova Infra-Red Experiment ” ( DESIRE ) , is designed to fit within 6 months of Euclid observing time , with a dedicated observing programme . We simulate the SN events as they would be observed in rolling-search mode by the various instruments , and derive the quality of expected cosmological constraints . We account for known systematic uncertainties , in particular calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light curves . Using conservative assumptions and a 1-D geometric Planck prior , we find that the ensemble of surveys would yield competitive constraints : a constant equation of state parameter can be constrained to \sigma ( w ) = 0.022 , and a Dark Energy Task Force figure of merit of 203 is found for a two-parameter equation of state . Our simulations thus indicate that Euclid can bring a significant contribution to a purely geometrical cosmology constraint by extending a high-quality SN Ia Hubble diagram to z \sim 1.5 . We also present other science topics enabled by the DESIRE Euclid observations .