How to check for websocket connections?
If you don't need to automate the websocket inspection (i.e. doing it "by hand", one website by one, with your own browser) :
You can open the Chrome console (CTRL+SHIFT+J) then under the network tab you'll find the websockets currently opened and you'll be able to see the frames that have been exchanged with the server.
But it's not clear if you want to do that by yourself with your browser or if you want to automate the process to automatically scan some websites to look for websocket usage (i.e. using a script) ?
If so, maybe you should take a look at the Chrome driver or even a testing framework like geb (or Selenium, Cucumber, ...).