Magnetic fields play a crucial role throughout stellar evolution, regulating angular momentum, channelling accretion, and launching jets and outflows. While the magnetic properties of Classical T Tauri Stars (CTTS) are well characterised, those of their progenitors, Class I and Flat-Spectrum (FS) protostars, remain poorly constrained due to observational challenges linked to their embedded nature. We aim to detect and characterise large-scale magnetic fields in a sample of Class I and FS protostars, which are expected to host strong dynamo-generated fields. Using SPIRou, a high-resolution near-infrared spectropolarimeter, we analysed polarised spectra and applied the Least Squares Deconvolution (LSD) technique to extract magnetic signatures and measure longitudinal fields from Stokes V profiles. We report new detections of large-scale magnetic fields in 5 FS protostars. Including the previously known magnetic FS protostar V347 Aur, 40% of our sample (15 objects) is confirmed to be magnetic. These stars exhibit clear Zeeman signatures, with longitudinal field strengths ranging from ~80 to ~200 G. The remaining targets show no detectable Stokes V signature, with upper limits on dipolar fields between 500 G and >5 kG. These results indicate that Class I and FS protostars can host large-scale magnetic fields, possibly weaker than in CTTS, supporting the idea that magnetic processes are already active during the main accretion phase and may influence star-disk interactions from the earliest stages.