With the best of modern standard lasers, high-energy colliders from electron beams of E larger than 250 GeV are possible at the expense of photon luminosity, i.e. 10 times lower than for photon colliders at c.m. energies below 0.5 TeV. This Snowmass21 Contributed Paper shows how Free Electron Lasers (FEL) pave the way for High Energy & High Luminosity colliders. We present and assess a conceptual design study of the Free Electron Laser that would be required for high luminosity colliders as second interaction region of 0.5 TeV to 10 TeV c.m. colliders.