Colloidal quantum dots display a wide range of novel optical properties that could prove useful for many applications in photonics. Here, we report the enhancement of fluorescence emission from colloidal quantum dots on the surface of two-dimensional photonic crystal slabs. The enhancement is due to a combination of high-intensity near fields and strong coherent scattering effects, which we attribute to leaky eigenmodes of the photonic crystal. By fabricating two-dimensional photonic crystal slabs that operate at visible wavelengths and engineering their leaky modes so that they overlap with the absorption and emission wavelengths of the quantum dots, we demonstrate that the fluorescence intensity can be enhanced by a factor of up to 108 compared with quantum dots on an unpatterned surface.