How should I sense the presence of current in Solar-Supercapacitor circuit?
I'd suggest that one solution may be to use a high (you could also do low side) current monitor IC such as the TI INA21x series. 

The circuit would look like this:



I'd also suggest that the diode you show (1N4148) should be replaced with a Schottky version such as a 1N5817

If you don't need to know the absolute current flowing, only that 'some positive' current is flowing you could even use the INA212 as a switch to measure just the Vf of the diode to infer current is indeed flowing. 

The INA21x Vout = (I(load) * R(shunt)) * gain + V(ref)

Since I(load) * R(Shunt) is just a voltage, you could substitute the diode Vf.
If you don't offset by a V(ref), then the output voltage is simply Vf * gain.

The Schottky diode has a very low barrier potential, so you can actually see current flows down to around 0.1 V.
The graph below shows that at 100 mA you can expect a Vf of only 0.25 V on the 1N5817. This would work as a switch indicator down in the &lt; 100 mA region.