Femtosecond laser point-by-point writing is a commonly used method for fabrication of Fiber Bragg Grating sensors dedicated to harsh environments, such as high temperature or irradiation. In addition, a femtosecond laser platform allows for inscription of compact fiber optic diffraction gratings that consist of micro-voids or filaments formed into the fiber core and cladding by focusing laser pulses using microscope objectives. Light propagating in the fiber is coupled to radiation modes due to Mie scattering, thus providing wavelength dispersion in free space. Chirping the grating period further allows focusing of the outcoupled light in a given plane. Such an all-fiber focusing grating forms a compact photonic device permitting its use for FBG sensor interrogation. In this paper, fabrication of such spectrometers operating at 850 and 1550 nanometers is described. A characterization setup allowing measurements of spectra of FBGs at those wavelength bands is presented, and results corresponding to various focusing distances, grating lengths and chosen microscope objectives are exposed. Azimuthal distribution of scattered light is discussed, as well as focusing distance versus grating period chirp and spectrometer resolution versus grating length. Finally, spectra reflected by pointby- point FBG sensors are presented, thus demonstrating the great potential interest of such gratings for FBG interrogation.