The curve modifier is a bit of a tricky one, as it requires you to spend a bit more attention to the orientation of the source object. To start with, make the local axis of the object which you want to bend visible in the Object tab / Display section:
In your case, the positive Z Axis is pointing up the direction of the Helix, and this is the direction which you want to deform. Next, Handle the origins. The Origin of the Helix should be at the starting point of the deformation. If it is not, you need later on to locally translate it along its local Z axis to match up the curve (in your file it was centered on the object). If you place it like in this screenshot, you can skip the translation step:
The highlighted axis are the one from the helix, the dark ones the axis of the curve you provided.
Then, make sure that the origin of the curve is at the origin of the helix. You can snap them together using the commands in the Shift S menu:
Now add the curve modifier, and set the deformation direction to Z:
As lemon rightfully anticipated, the curve radius is too small to get nice deformation. Ease out the curve a bit more to fix it.
Blend File is here: