Trying to understand inductance while driving a laser module
Since the comments cleared up the problem, and you've verified that my suggestions were correct, I'll make an answer of them.

First off, is has nothing to do with "inductance."  Inductance is associated with coils (also known as inductors.)  Your body does act like a mixture of various passive components - it has resistance and capacitance, and if you measure it right it has inductance as well.  The most relevant thing here, however, is resistance.

When you touch the gate of the FET with one hand, and the laser module with the other, you are most likely supplying 5V to the gate from the laser through your body.  

You need to pull the gate to a higher voltage to make it "switch" properly.  3.3V (which you used previously) isn't high enough to make the  2N7002 conduct well.  It is specified at 10V difference between gate and source.

With your hands in there, you are getting 5V from the laser to the gate.  That is enough to open up the FET and get the laser lit brightly. Your body is playing the part of the pull up resistor.

3.3V seems to be too little.  5V is better, but I expect the transistor still isn't fully on.

You might ought to look into an FET with a lower Vgs.  Maybe one of the "logic level"  FETs that are available.