Free-electron lasers (FELs) are a unique source of light, particularly in the x-ray domain. After the success of FELs based on conventional acceleration using radio-frequency cavities, an important challenge is the development of FELs based on electron bunching accelerated by a laser wakefield accelerator (LWFA). However, the present LWFA electron bunch properties do not permit use directly for a significant FEL amplification. It is known that longitudinal decompression of electron beams delivered by state-of-the-art LWFA eases the FEL process. We propose here a second order transverse beam manipulation turning the large inherent transverse chromatic emittances of LWFA beams into direct FEL gain advantage. Numerical simulations are presented showing that this beam manipulation can further enhance by orders of magnitude the peak power of the radiation.