Why json_encode() return keys values twice (index key and string key)?

you have to use PDO::FETCH__ASSOC as a parameter

$req = $bdd->prepare("SELECT mail,description FROM identifiant WHERE mail = :mail AND pass=:pass");
        if ($req->execute(array(
                    'mail' => $_COOKIE['mail'],
                    'pass' => $_COOKIE['pass']))) {
            header('Content-type: application/json');

  return  json_encode($req->fetchAll(PDO::FETCH_ASSOC));

}

use this:

PDO::FETCH_ASSOC: returns an array indexed by column name as returned in your result set

PDO::FETCH_BOTH (default): returns an array indexed by both column name and 0-indexed column number as returned in your result set

PDO::FETCH_BOUND: returns TRUE and assigns the values of the columns in your result set to the PHP variables to which they were bound with the PDOStatement::bindColumn() method

PDO::FETCH_CLASS: returns a new instance of the requested class, mapping the columns of the result set to named properties in the class. If fetch_style includes PDO::FETCH_CLASSTYPE (e.g. PDO::FETCH_CLASS | PDO::FETCH_CLASSTYPE) then the name of the class is determined from a value of the first column.

PDO::FETCH_INTO: updates an existing instance of the requested class, mapping the columns of the result set to named properties in the class

PDO::FETCH_LAZY: combines PDO::FETCH_BOTH and PDO::FETCH_OBJ, creating the object variable names as they are accessed

PDO::FETCH_NUM: returns an array indexed by column number as returned in your result set, starting at column 0

PDO::FETCH_OBJ: returns an anonymous object with property names that correspond to the column names returned in your result set

PDOStatement::fetch

return json_encode($req->fetchAll(PDO::FETCH_ASSOC));

It's not json_encode, it's because your PDO instance's fetch mode is set to PDO::FETCH_BOTH. See the documentation for PDOStatement::fetchAll's fetch style.