As the replies to your question will attest, viewing Netflix via Contour *will* require the additional fee of a paid Netflix subscription, and viewing content there *will* be added to your monthly data use.
If watching Netflix is something you're considering, I would strongly recommend buying an external streaming device (your choice: Apple TV, Amazon, Chromecast or Roku).
If you DO make that decision and can connect that device with ethernet cables I would also recommend buying a streaming device that has an ethernet port. This will provide a much more stable connection than WiFi.
I am a Netflix subscriber who views it along with Hulu and Amazon titles through a Roku with an ethernet port. I gave up after a couple of attempts to watch Netflix via Cox Contour. It loads much too slow for me. Frustratingly slow. Compared to Contour, we're literally talking tortoise and hare.