Building on Rob Kennedy's answer and using NDde

Copyusing NDde.Client;

class Test
{
        public static string GetFirefoxURL()
        {
            DdeClient dde = new DdeClient("Firefox", "WWW_GetWindowInfo");
            dde.Connect();
            string url = dde.Request("URL", int.MaxValue);
            dde.Disconnect();
            return url;
        }
}

NB: This is very slow. It takes a few seconds on my computer. The result will look something like this :

Copy"http://stackoverflow.com/questions/430614/get-firefox-url","Get Firefox URL? - Stack Overflow",""

More info on browser DDE here.

getting the URL from a sidebar or popup

To retrieve the URL from a sidebar or popup requires tab permissions

"permissions": [
    "tabs"
  ]

then you need to find the tab you want. If you just want the active tab this would work fine, for anything more advanced I'd look here.

function getPage(){
  browser.tabs.query({currentWindow: true, active: true})
    .then((tabs) => {
      console.log(tabs[0].url);
  })
}

getting the URL from injected javascript

If you want the URL for a background task I suggest this method as you do not need permissions.

this will give you a background script and then inject a script onto almost any webpage on the internet.

"background": {
    "scripts": ["background.js"]
},

"content_scripts": [
    {
      "matches": ["https://www.*"],
      "js": ["modify-page/URL.js"]
    }
  ],

this will be injected into webpages through the URL js and will send a message to your background js to use.

var service= browser.runtime.connect({name:"port-from-cs"});

service.postMessage({location: document.URL});

This code is in your background js and will collect each new page's url as it changes.

var portFromCS;

function connected(p) {
  portFromCS = p;
  portFromCS.onMessage.addListener(function(m) {
    if(m.location !== undefined){
      console.log(m.location);
    }
  });
}

browser.runtime.onConnect.addListener(connected);

You can do it like:

firefox -new-tab "https://www.useotools.com"

OR with full path

"C:\Program Files\Mozilla Firefox\firefox.exe" -new-tab "https://www.useotools.com"