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ABSTRACT The fuzzy dark matter (FDM) scenario has received increased attention in recent years due to the small-scale challenges of the vanilla Lambda cold dark matter (ΛCDM) cosmological model and the lack of any experimental evidence for any candidate particle. In this study, we use cosmological N-body simulations to investigate high-redshift dark matter haloes and their responsiveness to an FDM-like power spectrum cutoff on small scales in the primordial density perturbations. We study halo density profiles, shapes, and alignments in FDM-like cosmologies (the latter two for the first time) by providing fits and quantifying departures from ΛCDM as a function of the particle mass m. Compared to ΛCDM, the concentrations of FDM-like haloes are lower, peaking at an m-dependent halo mass and thus breaking the approximate universality of density profiles in ΛCDM. The intermediate-to-major and minor-to-major shape parameter profiles are monotonically increasing with ellipsoidal radius in N-body simulations of ΛCDM. In FDM-like cosmologies, the monotonicity is broken, haloes are more elongated around the virial radius than their ΛCDM counterparts and less elongated closer to the centre. Finally, intrinsic alignment correlations, stemming from the deformation of initially spherically collapsing haloes in an ambient gravitational tidal field, become stronger with decreasing m. At z ∼ 4, we find a 6.4σ-significance in the fractional differences between the isotropized linear alignment magnitudes Diso in the m = 10−22 eV model and ΛCDM. Such FDM-like imprints on the internal properties of virialized haloes are expected to be strikingly visible in the high-z Universe.