Why does my mic behave like an antenna only when I touch it?
Your mic always "behaves like an antenna." The capacitance from your body only affects the resonant frequency of the "antenna." The resulting resonant frequency just happens to be in the AM broadcast band. This is why, when you touch the mic, everyone starts speaking French. 

When you're not touching the mic, the "antenna" is tuned to best receive some other frequency than the Voice of Les Habs.

See this discussion on how RF gets into audio preamps.