I decided to send another answer with more specifications.

Step 1
Create your buttons with data-lang attribute with the value of your language. Let's name it channels.php:

<!-- data-lang="en": English -->
<button class="btn" data-lang="en">English</button>

<!-- data-lang="fa": Persian (farsi) -->
<button class="btn" data-lang="fa">Persian</button>

<!-- data-lang="fr": French -->
<button class="btn" data-lang="fr">French</button>

Step 2
Add some jQuery to your channel.php file:

<script>
    $(".btn").click(function(){
        // Get data-lang attribute from clicked element
        let lang = $(this).attr("data-lang");

        // Send a GET request to your ajax.php file
        $("#page").load("ajax.php?lang=" + lang);
        // or it can be the URL of your ajax file
        // it's something like this: http://example.com/ajax.php?lang=en
    });
</script>

Step 3 Now your ajax.php should be something like this:

# check if the lang parameter is set in the URL or set "en" language by default
$lang = $_GET['lang'] ?? "en";

# If the language is English
if( $lang == "en" ){
    echo "English content";
}
# If the language is Farsi
else if( $lang == "fa" ){
    echo "Farsi content";
}
# If the language is French
else if( $lang == "fr" ){
    echo "French content";
}

You have to replace your content with echo "... content"; for each language.

I'm not sure how much you know about php, but you can put some HTML codes between PHP without using echo, just close PHP tag, write your HTML, then reopen php tag:

<?php

# some php codes

?>

<h1>HTML content</h1>

<?php

# Some more php contents

?>

in this case, it's something like this:

if( true ){
   # Closing PHP tag
   ?>
   <!-- Writing HTML contents -->
   <h1>HTML content</h1>
   <?php
   # Then reopen PHP tag
}

Finally, you can put your embedded HTML Youtube player instead using echo:

if( $lang == "en" ){
    ?>
       <iframe width="560" height="315" src="https://youtube.com/vide/url?autoplay=1" frameborder="0" allowfullscreen></iframe>
    <?php
}

I hope this was helpful

I'm not sure I understand what you are trying to do, but you should get the page URL from its attribute.

<script language="javascript">
$(function(){
  $(".button").click(function(){
    var address = $(this).attr("data-address");
    $("#pantalla").load(address);
  });
});
</script>

<button class="button" data-address="/screen-eng.php">Music videos</button>

<button class="button" data-address="/screen-mov.php">Movie clips</button>
...

1. Add data-address attribute with value of your page address

2. Get current attribute by using $(this).attr("data-address")

But I recommend to use this code instead:

<!-- index.html -->
<button class="btn" data-lang="en">English</button>

<button class="btn" data-lang="fa">Persian</button>

<button class="btn" data-lang="fr">French</button>

<div id="page"></div>

<script>
    $(".btn").click(function(){
        let lang = $(this).attr("data-lang");
        $("#page").load("ajax.php?lang=" + lang);
    });
</script>

then on your server-side handle the request:

// ajax.php
# check if the lang parameter is set in the URL or set "en" language by default
$lang = $_GET['lang'] ?? "en";

if( $lang == "en" ){
    ?>
      <iframe width="560" height="315" src="https://youtube.com/embed/D6Ac5JpCHmI?autoplay=1" frameborder="0" allowfullscreen></iframe>
    <?php
}
else if( $lang == "fa" ){
    ?>
      <iframe width="560" height="315" src="https://youtube.com/another/video?autoplay=1" frameborder="0" allowfullscreen></iframe>
    <?php
}
else if( $lang == "fr" ){
    ?>
      <iframe width="560" height="315" src="https://youtube.com/one/more/video?autoplay=1" frameborder="0" allowfullscreen></iframe>
    <?php
}

Edit

Just add some youtube embedded video player in your PHP and manage them by sending GET to your server.

There is no need to create multiple pages for each video, just add your video URL like this code and get whichever you want by sending a GET request like this:

http://example.com/ajax.php?lang=en