Robust spin Hall effects (SHE) have recently been observed in nonmagnetic heavy metal systems with strong spin-orbit interactions. These SHE are either attributed to an intrinsic band-structure effect or to extrinsic spin-dependent scattering from impurities, namely, side jump or skew scattering. Here we report on an extraordinarily strong spin Hall effect, attributable to spin fluctuations, in ferromagnetic FexPt1-x alloys near their Curie point, tunable with x. This results in a dampinglike spin-orbit torque being exerted on an adjacent ferromagnetic layer that is strongly temperature dependent in this transition region, with a peak value that indicates a lower bound 0.34±0.02 for the peak spin Hall ratio within the FePt. We also observe a pronounced peak in the effective spin-mixing conductance of the FM/FePt interface, and determine the spin diffusion length in these FexPt1-x alloys. These results establish new opportunities for fundamental studies of spin dynamics and transport in ferromagnetic systems with strong spin fluctuations, and a new pathway for efficiently generating strong spin currents for applications. © 2018 American Physical Society.