The inductor (and its parasitic capacitance and resistance) combined with the capacitance and inductance of the antenna form a crude tuned circuit. Obviously, the length, shape, and position of the antenna will affect the impedance of the antenna, and the resonant frequency of the tuned circuit. This form of tuning is "iffy" at best, but if adjusted properly (through a good deal of experimentation) does offer some measure of selectivity from other surrounding EM fields at different frequencies.
This detector circuit is not very sensitive to begin with, so I question the need for the inductor and would go without it (and the resistor). Due to its poor sensitivity, it is not likely you will find use for the detector anywhere other than where the field strength from the source you are measuring is much greater than that from any other source. The inductor will only tend to attenuate the signal at the antenna connection and this detector can use all the sensitivity you can give it.
Don't plan on making accurate measurements of field strength with this circuit, but rather, relative measurements between various locations in the field.
The tuned portion of the circuit does not have much relationship to the rest of the circuit. Ideally, you would use a good antenna, which is already cut for the frequency of interest (providing selectivity), with a known real impedance and replace the inductor with a resistor to match that impedance.