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Exploring the properties of exoplanets near or inside the radius valley provides insights on the transition from the rocky super-Earths to the larger, hydrogen-rich atmosphere mini-Neptunes. Here, we report the discovery of TOI-1452 b, a transiting super-Earth ($R_{\rm p} = 1.67 \pm 0.07$ R$_{\oplus}$) in an 11.1--day temperate orbit ($T_{\rm eq} = 326 \pm 7$ K) around the primary member ($H = 10.0$, $T_{\rm eff} = 3185 \pm 50$ K) of a nearby visual binary M dwarf. The transits were first detected by TESS, then successfully isolated between the two $3.2^{\prime\prime}$ companions with ground-based photometry from OMM and MuSCAT3. The planetary nature of TOI-1452 b was established through high-precision velocimetry with the near-infrared SPIRou spectropolarimeter as part of the ongoing SPIRou Legacy Survey. The measured planetary mass ($4.8 \pm 1.3$ M$_{\oplus}$) and inferred bulk density ($5.6^{+1.8}_{-1.6}$ g/cm$^3$) is suggestive of a rocky core surrounded by a volatile-rich envelope. More quantitatively, the mass and radius of TOI-1452 b, combined with the stellar abundance of refractory elements (Fe, Mg and Si) measured by SPIRou, is consistent with a core mass fraction of $18\pm6$ % and a water mass fraction of $22^{+21}_{-13}$%. The water world candidate TOI-1452 b is a prime target for future atmospheric characterization with JWST, featuring a Transmission Spectroscopy Metric similar to other well-known temperate small planets such as LHS 1140 b and K2-18 b. The system is located near Webb's northern Continuous Viewing Zone, implying that is can be followed at almost any moment of the year.