Do you eat cantaloupe or muskmelon at your house?
A few years ago I used some compost in my flower garden and surprise! I had a plant similar to yours growing amongst my marigolds. I let it keep growing, very sure it wasn't a weed. Like others have mentioned I thought it was a squash or cucumbers. It ended up being a muskmelon. We eat it for breakfast a lot and so some seeds had ended up in the compost, then my garden.
Unfortunately they require quite a long time to grow (80-90 days above 70 degrees F or something like that) so I never got to eat one of them. (I live in New England, so I would have had to start them much sooner and kept them warm)
Let it grow and see what you've got. If it is a muskmelon, and you're in a more friendly zone for melons than I, pinch off all but one or two fruits so they are nice and sweet, and keep them on pea gravel or elevate them off the ground some other way so they don't rot on the soil. Once they start to ripen (you will see the flesh beneath the web-like texture start to turn orange) only water enough to prevent wilting, to further increase the sweetness.