We present triple-axis neutron scattering studies of static and dynamic magnetic stripes in an optimally oxygen-doped cuprate superconductor, La₂CuO_4+y, which exhibits a clean superconducting transition at Tc = 42K. Polarization analysis reveals that the magnetic stripe structure is equally represented along both of the tetragonal crystal axes and that the fluctuating stripes display significant weight for in-plane as well as out-of-plane spin components. Both static magnetic order as well as low-energy fluctuations are fully developed in zero applied magnetic field and the low-energy spin fluctuations at ℏω = 0.3–10 meV intensify on cooling. We interpret this as an indication that superconductivity and low-energy spin fluctuations coexist microscopically in spatial regions which are separated from domains with static magnetic order.