Using canoe paddles to rig tarp shelters seems to be a common practice (e.g. see here or here). I would rig them as in the diagram below - as for an A-frame tarp shelter. I would expect you would need more than 1m height for the centre of the net so I would use the paddles whole not split.
The two paddles are on end, pointing up, with the top ends connected by a length of cord. Two further lengths of cord run from the top of each paddle at roughly 120 degrees to the centre cord, down to anchors on the ground.
This will give you plenty of height, though you will also need lots of space to set it up. A more compact setup may be possible with the two paddles lashed together at one end forming an inverted V over the bug net, and then a cord running from an anchor on one side to the point of the V and back down to an anchor on the other side (giving you something like a square pyramid). This provides much less height however.
Disclaimer: I am not a canoeist (I camp under a tarp on walking/running trips) so I don't know how well your paddles will stand up to this kind of abuse. A lightweight porous insect net shouldn't need a lot of tension on the cords however, so I would not expect any problems.