We performed small-angle neutron scattering (SANS) measurements on the helimagnetic spinel compound ZnCr₂Se₄. The ground state of this material is a multi-domain spin-spiral phase, which undergoes domain selection in a magnetic field and reportedly exhibits a transition to a proposed spin-nematic phase at higher fields. We observed a continuous change in the magnetic structure as a function of field and temperature, as well as a weak discontinuous jump in the spiral pitch across the domain-selection transition upon increasing field. From our SANS results we have established the absence of any long-range magnetic order in the high-field (spin-nematic) phase. We also found that all the observed phase transitions are surprisingly isotropic with respect to the field direction.