Is there a way to simply move the toolpath to the other side of the line?
You have two choices for this.
If you look where I've placed the red box in the first snip you will see the options for setting up a Profile toolpath. The Inside/Outside options apply when the selected vector is a closed shape, the Left/Right options apply when the selected vector is open, which is what you have.
One method is to simply select the other toolpath option (Left/Right) and recalculate the toolpath. If you make the toolpath visible by checking the box next to the toolpath name, you can see the toolpath in the 2D view. This is the path the center of the bit will follow and you can visibly see if it is on the side of the vector you want.
Since the left and right sides of an open vector is referenced to the end of the vector that is the start point, the second method involves node editing to change the start point. You would select the vector and use the icon or press N to enter node editing. The green node is the current start point and to change it you would hover the cursor over the black node at the other end of the vector and either press P to make this the start point or right click and select the action circled in the second picture.
If you haven't found them yet, there are some video tutorials on Cut2D found here:http://www.vectric.com/support/training-material.html
It is also worth the time to go through the FAQ's for Cut2D found here:http://support.vectric.com/faq
Hopefully this helps.