fiber optic output source for testing an embedded fiber bragg grating array
To really test the FBG you'll need to know what wavelength they are designed for and couple laser light into the fiber. Preferably you'd use the correct optics with similar numerical aperture and measure the relative intensity and the spectral output. Note that most FBG are used in single mode fibers which have low numerical aperture and are hard to couple light into if you don't have the right optics/mounts. If you're working in the infrared at telecomm wavelengths connectors and test fixtures are much much cheaper.

If you're ok with not testing them at the wavelengths they're designed for and just want to see if there is a break in the fiber couple in a visible laser diode and look for any hotspots or light leaking out which is indicative of a break in the fiber:

Choose a wavelength that's somewhat transmissive based on the transmission spectrum of the array. Since there are fc connectors on the end the easiest way to do this would be to buy an fc mounted lens designed to focus light into the fiber (although it won't be perfect because you'll be using the wrong wavelength). Mount the collimated laser diode source,  couple light into it into the fiber and look for any obvious leakage out of the fiber. You might be able to couple enough light in without a lens although I wouldn't count on it. If the laser is eye safe in a dark room then turn off the lights and let your eyes adjust.  

If you happen to have a spectrometer laying around you could characterize any broadband source you have then couple light from the source into the bragg grating and look at the output. Any peaks missing would be indicative of an reflection line. However, assuming this bragg grating is single mode (~5µm diameter core) this probably won't be very efficient and you might struggle to get enough light through the small fiber. Also, if you're out at the telecomm wavelengths (~1550nm) most spectrometers aren't designed to go out this far and won't work well or at all. If you can provide more specifics such as design spectrum, fiber length, core diameter someone might have some bright ideas.