Is it possible to estimate what the white noise floor should be, and after cross-correlation?
I assume you notation "^-7V" refers to a voltage noise level of $1E-7$ volts, and then when you say it is in the frequency domain, then I assume this is the average of the FFT magnitude for all the bins that are not part of your signal (the noise floor). This average noise level is completely dependent on the number of bins in your FFT.

I do not understand clearly what your processing would be to "cross-correlate in the frequency domain", but based on your results I assume you are simply multiplying and then taking an FFT (which is not "cross-correlate in the frequency domain). If this was the case, and it was a complex conjugate multiplication then you would get the cancellation you describe, and to the degree the input signals are correlated, and the system is matched then you would likely be seeing the noise floor of your instrument.  

Generally, when you perform an actual cross correlation between two noise signals, if it is the same noise at the same rms level, then the correlation result will go up in magnitude by a factor of 2. If the two noise sources are independent and identically distributed, then the correlation result will go up by $\sqrt{2}$. (Independent noise sources sum directly by their variance, correlated noise sources sum directly by their standard deviations).