Interrupt fires multiple times
Two other possible problems, apart from what Jake C has adressed in his answer are:

1. Hardware bounce

If your signal from the sensor isn't a clean transition from high to low but rather "bouncy" (see image below). The microcontroller will register multiple transitions in the meantime.



Solution to this would be to add a small capacitor (wil slow it down though) or add debouncing code... Best would be to get a "clean" sensor.

2. Floating contact


  When I even move my finger close to the wire running to PIN2 the interrupt fires.


That kinda seems like it's a floating contact, where it's not really connected to anything.

This is usually solved by using a pullup/pulldown resistor. Or maybe there is something wrong with the connection.



Also:


  Maybe due to the type of sensor?


You should note the part number of the sensor or link a datasheet, so we can see if it's typical behaviour for this type of sensor.