Curl options equivalent to "useDefaultCredentials" by Net.Webclient

I try to access to the web with curl in a php script :

$ch = curl_init();

curl_setopt($ch, CURLOPT_URL, "https://www.google.fr");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);

$result = curl_exec($ch);
if (curl_errno($ch)) {
    echo 'Error:' . curl_error($ch);
}

curl_close ($ch);

It returns :

Failed to connect to www.google.fr port 443: Connection refused

That's normal, I'm behind a proxy, which require my Windows credentials (NTLM) to allow internet trafic.

In MS Powershell, this works :

$request = New-Object System.Net.WebCLient
$request.UseDefaultCredentials = $true
$request.Proxy.Credentials = $request.Credentials
$request.DownloadFile($url, $path)

Using the "DefaultCredentials" (= Windows Credentials) and send them to the proxy allows me to access to the web. But I don't now how it works.

If I navigate using Firefox, Firefox always add a Proxy-Authorization header, with value : Negociate blablablablababalazdlad...

I want to transpose the .NET useDefaultCredentials solution to cURL, I tried :

$ch = curl_init();

curl_setopt($ch, CURLOPT_URL, "https://www.google.fr");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);

curl_setopt($ch, CURLOPT_HTTPAUTH, CURLAUTH_NTLM );
curl_setopt($ch, CURLOPT_PROXYAUTH, CURLAUTH_NTLM );

$result = curl_exec($ch);
if (curl_errno($ch)) {
    echo 'Error:' . curl_error($ch);
}

curl_close ($ch);

Without success