WebClient 403 Forbidden

403 may also be caused by TLS issues. To verify, you should check the text of the WebException.Response object.

     catch (WebException ex)
     {
        if (ex.Response != null)
        {
           var response = ex.Response;
           var dataStream = response.GetResponseStream();
           var reader = new StreamReader(dataStream);
           var details = reader.ReadToEnd();
        }
     }

If it is TLS then try adding this to your code to force TLS1.2.

For .net4:

ServicePointManager.SecurityProtocol = (SecurityProtocolType)3072;

For .net4.5 or later:

ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12;

I had this problem trying to download an image from a SharePoint site url. In my case setting the user-agent to Other or blank in the header wasn't enough, I had to set the user-agent as follows instead:

client.Headers.Add("user-agent", " Mozilla/5.0 (Windows NT 6.1; WOW64; rv:25.0) Gecko/20100101 Firefox/25.0");

That solution came from this answer.