It sounds like the motor is working, if you can hear it. .. so don't worry about the switch. I just had a dicky switch in my sister's Megane once, which didn't work at all using the driver's switch... but the connector did fit on the other switch in the "passenger" switch (on the driver's door) so I could tell it was the switch.
If the motor is working and the glass isn't moving then the mirror motor could be broken or the control arms may have become detached. You'll need to remove the glass to have a look.
The motor will probably have a nylon cog to turn the levers that move the glass pad. Nylon isn't particularly robust, so if the mirror glass/pad was sticky or needed more force to move it once (e.g. if it was frozen to the mirror body etc.) then the teeth may have stripped and now there's no teeth on the cog to turn the pad. In this case you'll probably need a new mirror (or at least the working internals from a second-hand one).
The other possibility is that the motor is turning fine but how it operates on the pad isn't working (e.g if there is an arm or lever .. usually held together by a ball socket) that has come apart. I've got an old mirror somewhere to have a look .. It may be possible to re-clip it.. but if the socket is loose/damaged, then again, you'll need a new "internals".
Ralf S.