The mic is an electret type, not a simple condenser type that needs a 48V supply and an impedance converter.
The simplicity of this transmitter causes performance problems and it has errors that will cause it to sound awful:
1) It is missing a voltage regulator so the radio frequency will change as the battery voltage runs down.
2) It is missing an RF amplifier/buffer so of course the frequency changes if something moves towards or away from the antenna.
3) The 100nF capacitor kills audio frequencies above 533Hz. My FM transmitter uses only 470pF.
4) There is no mic preamp so it will not sound loud enough.
5) It is missing pre-emphasis (audio high frequencies boost) that all FM radio stations have then the de-emphasis used in all FM radios will cause received high audio frequencies to sound muffled.
6) It is missing a power supply decoupling (bypass) capacitor.