Detecting low currents in high current industrial environment
120A is at least 6mm2 of cable.

A current transformer is then the typical way to measure current. However, that is very big. Especially for three. And may be expensive at the precision you require.
You can get a bit smaller with a hall sensor current transformer. 
Such as LEM LZSR.



When even that won't fit then you can go looking for separate magneto resistive current sensors. At cost of a significantly more complicated design, validation and calibration.
Sensitec and Allegro Microsystems are famous for these.



Using a traditional discrete hall sensor will probably not work reliably at the low ranges you are looking for. If you can find them with proportional output at all.