An FM transmitter operates at the very high frequency of about 100MHz. Wires at that frequency have series inductance and parallel capacitance so it won't work on a breadboard. The wires must be very short at such a high frequency.
Use a pcb or make it with very short wires on stripboard.
Your transistors don't look like modern 2N3904 ones, they look like they are in a very old metal case. What part number are they?
I don't see the coil in your picture, it should look like mine.
I also don't see the 4-40pF tuning trimmer capacitor in your picture.
My FM transmitter looks like this: