Guess what? If the 100MHz oscillator was designed properly to be powered from only 3V then C7 completely feeds the entire oscillation signal to ground. Remove C7.
Yes, the value of C6 is too large, my similar circuit uses 30pf but 150pF works better.
Your R3 should also be removed since it reduces the base voltage of Q1 so low that some transistors will not work, especially if the battery voltage is a little low.
Your value of R5 is very low, my similar circuit uses 220 ohms.
Instead of mixing left and right signals, your very low values for C1 and C2 are not passing audio signals but are passing only ultra-sonic signals to the very high value of C3 that shorts them to the positive supply. Use two 4.7k resistors with the left channel feeding one and the right channel feeding the other, then their other ends are joined together to mix the two channels and feed a 1uF coupling capacitor to the base of Q1.
Change the value of your C3 to 470pF that my similar circuit uses and connect it to ground instead of to the positive supply. Your Q2 is biased poorly like I was taught to never do because each transistor has a different hFE. Use 39k between its base and emitter instead.
All FM radio stations use pre-emphasis (treble frequencies boost) and all FM radios use matching de-emphasis to cut the high frequencies down to normal and reduce hiss. Your circuit is missing pre-emphasis so it will sound like your stereo with its treble tone control turned all the way down.
I agree that the very high radio frequency circuit will not work if built on a breadboard. Mine is built compactly on a stripboard.
Here is your partially fixed circuit and my circuit that works well and sounds perfect, except its radio signal is strong enough to cover a real radio station which is illegal: