Last year, my pumpkins immediately staged an escape from their designated garden bed. One grew out onto the lawn and headed for the apple tree. The other one grew a side branch -- both branches climbed the garden fence, and refused to come down.
One branch grew two pumpkins balanced on the top edge of the wire fence. They had grown in such a way that the vine itself was supporting their bottoms. Only thing I had to do was to stuff some straw between the pumpkins and the wire fence to keep the fruits from getting bruised. The other branch reached up above the wire garden fence to the 5' PVC picket fence, and proceeded to grow along the top rail.
This one also grew two pumpkins, but without regular places for the tendrils to hold onto, the vine itself was barely hanging on (I wove the vine along the top of the pickets), so I supported the fruits with slings out of one of my kid's old nylon tights that were tied onto the pickets above the top rail.