Your event in event.preventDefault is undefined. You have to define it in the function that you call it in:

$("#platba").submit(function(event) {
  event.preventDefault();
});

Here is your corrected code that also works in Firefox (tested it myself on jsfiddle): https://jsfiddle.net/duzwo5bk/7/

Here is the code. Note: it doesn't work here because you cannot do popups from these snippets on StackOverflow

I also fixed the ID of your third radio :)

$(document).ready(function() {
  $("#platba").submit(function(event) {
    event.preventDefault();
    var loc = $('input[name="radio"]:checked').val();
    window.open(loc, '_blank');
    //self.close ();
  });
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<form id="platba">
<label class="c-input c-radio">
  <input id="radio1" name="radio" type="radio" value="https://www.paypal.com/uk/webapps/mpp/home">
  <span class="c-indicator"></span>
  <img src="img/payments/paypal.png" width="80" style="margin-top:-5px">&nbsp; Paypal
</label>
<br />
<br />
<label class="c-input c-radio">
  <input id="radio2" name="radio" type="radio" value="http://www.mbank.cz/osobni/">
  <span class="c-indicator"></span>
  <img src="img/payments/mbank.png" width="80" style="margin-top:-5px">&nbsp; mBank
</label>
<br />
<br />
<label class="c-input c-radio">
  <input id="radio3" name="radio" type="radio" value="http://example.com/platebnikarta">
  <span class="c-indicator"></span>
  <img src="img/payments/visa_mastercard.png" width="80" style="margin-top:-5px">&nbsp; Platební karta
</label>
<hr>

<button type="submit" class="btn btn-primary">Pokračovat v placení</button>
</form>

It certainly works for me in firefox. Could it be a popup-blocker?

You need to force the expresion to not return a value:

javascript:void(window.open(...))

Change your code a little bit like this

<script type="text/javascript">
 var _open = window.open("link.php", "_blank");
  if (_open == null || typeof(_open)=='undefined')
    alert("Turn off your pop-up blocker!");
  else
</script>

This should work now. The problem was that you're overwriting the window.open function using the global variable open

Actually, the W3Schools documentation linked to by gabriel1836 is only a very very brief summary of functions.

And Oddly, mozilla's own developer reference CONTRADITCS this logic.

MDC / DOM / Window.open

var WindowObjectReference = window.open(strUrl, 
              strWindowName [, strWindowFeatures]); 

If a window with the name strWindowName already exists, then, instead of opening a new window, strUrl is loaded into the existing window. In this case the return value of the method is the existing window and strWindowFeatures is ignored. Providing an empty string for strUrl is a way to get a reference to an open window by its name without changing the window's location. If you want to open a new window on every call of window.open(), you should use the special value _blank for strWindowName.

However, the page also states that there are many extensions that can be installed that change this behaviour.

So either the documentation mozilla provides for people targeting their own browser is wrong or something is odd with your test system :)

Also, your current A-Href notation is bad for the web, and will infuriate users.

  <a href="http://google.com"  
     onclick="window.open( this.href, 'windowName' ); return false" >
     Text
  </a>

Is a SUBSTANTIALLY better way to do it.

Many people will instinctively 'middle click' links they want to manually open in a new tab, and having your only href as "#" infuriates them to depravity.

The "#" trick is a redundant and somewhat bad trick to stop the page going somewhere unintended, but this is only because of the lack of understanding of how to use onclick

If you return FALSE from an on-click event, it will cancel the links default action ( the default action being navigating the current page away )

Even better than this notation would be to use unintrusive javascript like so:

 <a href="google.com" rel="external" >Text</a>

and later

 <script type="text/javascript">
 jQuery(function($){ 
        $("a[rel*=external]").click(function(){ 
            window.open(this.href, 'newWindowName' ); 
            return false; 
        });
 }); 
 </script>

try parent.window.opener instead of window.opener

Source: window.opener is null in firefox