The advice you've received so far is exactly what I would have said - you do need bias binding,but you can do it as French fold if you want. I have done French fold (normal double-layer quilt binding) on curves when I wanted the extra durability of a double layer, and it worked out fine.
One thing I haven't seen mentioned is that you have marked your sewing line on the quilt. It's much easier to mark where the edge of the binding should go - you won't be able to see the stitching line once you place the binding on top, so the edge line is easier to follow.
Good luck!