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I changed the function and it works. For those who need it, the code is not perfect but it works for the product list.

For prestashop 1.7.6.5 and a shop without tax (adapt for tax).

Create an override "Product.php" in /override/classes and copy this code :

<?php
    class Product extends ProductCore {

        public static function getMinSpecificPrice($id_product, $product_ratio)
        {
            $discount = DB::getInstance()->ExecuteS('
                SELECT MIN(price) AS min_price, from_quantity AS quantity
                FROM `'._DB_PREFIX_.'specific_price`
                WHERE id_product = '.$id_product.'');
    
            foreach ($discount as $data) {
                $counter = $data['quantity'];
                if ($counter > 1) {
                    $specificPrice = $data['min_price'];
                    $specificPrice = round($specificPrice, 2);
                    if ($product_ratio != 0) {
                        $specificPrice = ($specificPrice / $product_ratio);
                        return $specificPrice;
                    } 
                }
            }
        }

        public static function getUnitPrice($product_price_tax_exc, $product_ratio)
        {
            if ($product_ratio != 0) {
                $unitPrice = $product_price_tax_exc / $product_ratio;
                return $unitPrice;
            }
        }
    }

getMinSpecificPrice() will find out if a specific price exists and recover the lowest price.

getUnitPrice() will calculate and display the price per unit in the event that you sell a product by package.

Next in yourtheme\templates\catalog\_partials\miniatures\product.tpl, copy this code in the block 'product_price_and_shipping' :

              {assign var=specificPrice value=Product::getMinSpecificPrice($product.id_product, $product.unit_price_ratio)}
              {assign var=unitPrice value=Product::getUnitPrice($product.price_tax_exc, $product.unit_price_ratio)}
              {if $specificPrice}
                <span itemprop="price" class="price">A partir de {$specificPrice|string_format:"%.2f"|replace:'.':','} €</span>
              {else if $unitPrice}
                <span itemprop="price" class="price">{$unitPrice|string_format:"%.2f"|replace:'.':','} €</span>
              {else}
                <span itemprop="price" class="price">{$product.price}</span>
              {/if}

 Result :