As you don't need to bend the frame for a square or rectangular arch, I would suggest that you use sturdy material, such as 1/2" PVC or steel conduit. To give the arch some extra support you could tie monafilament line to the top of the arch and secure the other end to a hook in the ceiling. You will also need a base, similar to our balloon columns base, on either end.
In the video below they use rebars together with 1" PVC poles to create the arch frame. The advantage of this method is that the frame will be extra sturdy. The downside is that a 1" frame is difficult to cover completely with the 11" balloon clusters.
Hope that helps and good luck with your balloon arch!