Is this a correct method for fixed pattern noise correction?
The black image is the sum of a fixed pattern and dark noise (which most likely follows a normal distribution since it usually arises from current fluctuations). You want to subtract the fixed pattern, but not the dark noise - subtracting random noise from a signal simply increases the overall noise, and thus decreases signal quality.

To get a good estimate for the fixed pattern, you should capture a sizeable number of frames (say 25, though 100 will of course leave you with only half the noise), and average them. Since the dark noise is (should be) uncorrelated in time, it averages out, so that you're left with a low-noise fixed pattern that you can subtract from your future images, and that will not increase the noise in your image. 

Note that the fixed pattern usually depends on the exposure time (a CCD camera, for example, may accumulate electrons during shift operations), thus you'll have to do a calibration for each exposure time. If you vary exposure times often, and if it's feasible, you can set up your experiment to capture a series of dark frames after each experiment, which means that you get a calibration for each experiment.

If you subtract a low-noise (i.e. averaged) dark frame, you will get some negative values (because the dark noise occurring during image acquisition can have negative values), but the range of your image should not increase significantly. If it does, it is a sign that you have either not averaged enough dark frames, or that the fixed pattern has changed since you're using a different exposure time.