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Galaxy morphologies and shape orientations are expected to correlate with their large-scale environments, since they grow by accreting matter from the cosmic web and are subject to interactions with other galaxies. We extracted cosmic filaments in projection from the Euclid Quick Data Release 1 (covering 63.1 deg2) at 0.5 < z < 0.9 in tomographic slices of 170 comoving h −1 Mpc using photometric redshifts. Galaxy morphologies are accurately retrieved thanks to the excellent imaging resolution of the visible camera (VIS) of Euclid. The distribution of massive galaxies (M* > 1010 M⊙) in the projected cosmic web is analysed as a function of morphology measured from VIS data. Specifically, the 2D alignment of galaxy shapes with large-scale filaments is quantified as a function of Sérsic indices and masses. We find the known trend that more massive galaxies are closer to filament spines. At fixed stellar masses, morphologies correlate both with densities and distances to large-scale filaments. In addition, the large volume of this data set allows us to detect a signal indicating that there is a preferential alignment of the major axis of massive early-type galaxies along projected cosmic filaments. Overall, these results demonstrate our capabilities to carry out detailed studies of galaxy environments with Euclid, which will be extended to higher redshift and lower stellar masses with the future Euclid Deep Survey.