The question was kinda resolved in acejavelin's answer, but I just wanted to clarify that, sometimes, the ISP blocks connections to port 25 outbound, to limit spam from infected residential computers. If you are in France, as the host suggest, I know that free (an ISP) does that by default, but you can disable that on your customer panel.
The other major ISPISPs probably does it too, but I don't currently have the knowledge.
You should try to connect to some random mail server to see if it works.
You can also use telnet and http://portquiz.net/ to see blocked outbound ports, if any.