I found the solution. I have made a twig filter to get the path of the file uploaded with gaufrette. Solutions used for Amazon S3 and local.
app\config\services.yml
app.aws_s3.client:
    class: Aws\S3\S3Client
    arguments:
        -
            version: '%amazon_s3.version%'
            region: '%amazon_s3.region%'
            credentials:
                key: '%amazon_s3.key%'
                secret: '%amazon_s3.secret%'
html.twig
<a class="btn btn-primary" href="{{ pdf|get_path }}" target="_blank">Afficher le PDF actuel</a>
AppBundle\Resources\config\services.yml
app.twig_filter_extension:
    class: AppBundle\Twig\AppFilterExtension
    public: true
    arguments:
        - '%kernel.environment%'
        - '%prod_env%'
        - '%kernel.root_dir%'
        - '@router.request_context'
        - '@app.aws_s3.client'
        - '%amazon_s3.media_bucket%'
    tags:
        - { name: twig.extension }
AppBundle\Twig\AppFilterExtension.php
<?php
namespace AppBundle\Twig;
use Aws\S3\S3Client;
use Symfony\Component\Filesystem\Filesystem;
use Symfony\Component\Routing\RequestContext;
class AppFilterExtension extends \Twig_Extension
{
/**
 * @var string
 */
private $env;
/**
 * @var bool
 */
private $prodEnv;
/**
 * @var S3Client
 */
private $s3Client;
/**
 * @var string
 */
private $s3Bucket;
/**
 * @var Filesystem
 */
private $fileSystem;
/**
 * @var string
 */
private $rootPath;
/**
 * @var string
 */
private $baseUrl;
/**
 * AppFilterExtension constructor.
 *
 * @param string $env
 * @param bool   $prodEnv
 */
public function __construct(string $env, bool $prodEnv, string $rootDir, RequestContext $requestContext, S3Client $s3Client, string $s3Bucket)
{
    $this->env     = $env;
    $this->prodEnv = $prodEnv;
    $this->fileSystem = new Filesystem();
    $this->s3Client   = $s3Client;
    $this->s3Bucket   = $s3Bucket;
    $this->rootPath   = $rootDir . '/../web/';
    $this->baseUrl    = sprintf('%s://%s', $requestContext->getScheme(), $requestContext->getHost());
}
public function getFilters()
{
    return [
        new \Twig_SimpleFilter('get_path', [$this, 'getPath']),
    ];
}
/**
 * @param string      $uri
 * @param null|string $folder
 *
 * @return string
 */
public function getPath(string $uri, string $folder = null)
{
    if (
        (
            'dev' === $this->env ||
            false === $this->prodEnv
        ) &&
        true === $this->fileSystem->exists(str_replace('//', '/', sprintf('%s/%s/%s', $this->rootPath, ($folder ?? 'media'), $uri)))
    ) {
        return $this->baseUrl . str_replace('//', '/', sprintf('/%s/%s', ($folder ?? 'media'), $uri));
    }
    return str_replace('//', '/', $this->s3Client->getObjectUrl($folder ?? $this->s3Bucket, $uri));
}
/**
 * @return string
 */
public function getName()
{
    return 'app_filter_extension';
}
}