simple microphone - speaker circuit
Your circuit might almost work if you replace the microphone with a old carbon powder type.  This is what old telephones had in the mouthpiece.  That type of microphone looks like a variable resistor to the circuit, not the tiny voltage source your microphone probably is.  With a variable resistor, you can just put it in series with the speaker and a battery and probably hear sounds picked up by the microphone in the speaker.  If you can find a really old telephone with mechanical ringer, it might have a carbon mic in it.

Otherwise, microphones you get today produce a tiny varying voltage.  This must be amplified to drive a speaker.  Note that some types of microphones, called electrets, additionally need a few volts applied to it with a few k&Omega; imedance to produce that small varying voltage.  Electrets often come in small cartidges like what you show, so you may have such a mic.