Is there a term called "Fourier Beamforming"?
I'm guessing it's used in the following context. 

Assuming you have a physical source with some of an amplitude distribution in a plane: you can calculate the polar pattern of that source simply as the Fourier Transform of the amplitude distribution as a function of space (not time!).

Fourier Beamforming would be the inverse process: you start with the desired polar pattern and do an in inverse Fourier Transform: that gives you the desired in amplitudes as a function of space, i.e. it tells where to put sources or sensors and what weights to apply.