I don't really understand how FM narrow band is created, and at the same time I can't figure out how using this simple circuit of varactors (varicap diodes) we narrow the bandwidth.
Narrowband FM transmissions have a bandwidth that is about the same as the bandwidth of the modulating signal (the so-called modulation index is lower than 1). Wideband FM transmissions exceed the bandwidth of the signal (broadcast FM is 150kHz wide).
To narrow the modulation bandwidth for this circuit, you might reduce the influence of the varactor on the total capacitance of the resonant circuit.
The first three options require retuning of the circuit. So the simplest way to do it is to attenuate the modulation signal to bring the modulation index below 1.
Please note: Using the given component values the sweep will not be very big anyway. The few pf's from the varactors will not substantially change the total capacitance because C1's capacitance is almost a million times larger.