Counter in loop in foreach

EDIT

Ok so after better understanding your issue, I would not use a counter but a true/false flag that we switch when it’s been used. Try this code.

$cats = array('batiments-delevage', 'logements-bovin', 'stockages-deffluents', 'soins-et-hygiene');
$exclude_posts = array();
$active = true;
foreach( $cats as $cat ) :
  // build query argument
  $query_args = array(
  'category_name' => $cat,
  'posts_per_page'=> 1,
  'post_type'     => 'post',
  'post_status'   => 'publish',
  'meta_key'      => 'wpb_post_views_count', //custom field for view count
  'orderby'       => 'meta_value_num',
  'order'         => 'DESC'
);

// exclude post that already have been fetched
// this would be useful if multiple category is assigned for same post
if( !empty($exclude_posts) )
  $query_args['post__not_in'] = $exclude_posts;

// do query
$query = new WP_Query( $query_args );

if ($query->have_posts()) : // check if query have any post

  while ($query->have_posts()) : $query->the_post(); // start loop & set post global 
    // Get category slug parent info
    $category = get_the_category();
    $cat_slug = $category[0]->slug;
    $cat_name = $category[0]->name;
    $cat_url =  get_category_link( $category[0]->cat_ID );
    $post_date_month = get_the_date('M');
    $post_date_year = get_the_date('Y');


    $exclude_posts[] = get_the_ID();

?><div class="item <?php if( $active ){ echo 'active'; $active = false; } ?>">
  <header class="header-item">
    <a class="link-img" href="https://wordpress.stackexchange.com/questions/237694/<?php the_permalink(); ?>">
      <?php the_post_thumbnail('tab-slider', array( 'class' => 'img-responsive') ); ?>
    </a>
    <div class="date-box"><?php
      echo $post_date_month.'<br/>';
      echo '<small>'.$post_date_year.'</small>';
  ?></div>
  </header><!-- /header -->
    <div class="carousel-caption"> 
      <h4><a href="https://wordpress.stackexchange.com/questions/237694/<?php the_permalink(); ?>"><?php the_title(); ?></a></h4>
      <p class="meta-cat"><small><span class="inline-categ-icon visible-xs-block visible-sm-block icon-<?php echo $cat_slug;?>"></span>  Dans <a href="<?php echo $cat_url;?>" title="Voir les articles dans la rubrique « <?php echo $cat_name;?> » "><?php echo $cat_name;?></a></small></p>
      <p class="most-view-excerpt"><?php echo excerpt(27); ?></p>
    </div>
    <p><a class="read-more" href="https://wordpress.stackexchange.com/questions/237694/<?php the_permalink(); ?>" title="Lire notre article <?php the_title(); ?>">Lire le reportage</a></p>
  </div>
<?php endwhile; endif; ?>

<?php endforeach; ?>

ORIGINAL

You don’t need a counter to do the job, you can use the current_post property of the current object which returns the index of the current object

so instead of using

if ($i == 0)

try

if( 0 == $query->current_post )

and get rid of your counters

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