We report on the development of an ultrafast Transmission Electron Microscope based on a laser-driven cold-field emission source. We first describe the instrument before reporting on numerical simulations of the laser-driven electron emission. These simulations predict the temporal and spectral properties of the femtosecond electron pulses generated in our ultrafast electron source. We then discuss the effects that contribute to the spatial, temporal and spectral broadening of these electron pulses during their propagation from the electron source to the sample and finally to the detectors of the electron microscope. The spectro-temporal properties are then characterized in an electron/photon cross-correlation experiment based on the detection of electron energy gains. We finally illustrate the potential of this instrument for ultrafast electron holography and ultrafast electron diffraction.