Well unless you have a better idea, my project is a card game, and I intend the player to be able to interact with the game scene at all times ^^ (The player interacts only with the other player, there's no other people involved.) I didn't know there was a FAQ, so I read it and it made me install Wireshark. I could check that a frame (or whatever it's called) was indeed sent from the client to the server, and inside that frame was what I had written. (I wrote an std::string in that packet, and I could find and read it on Wireshark.) Wireshark spotted and listed that frame both from the client's computer, and from the server's.
Unfortunately, my socket keeps returning NotReady on the server's end. I must be missing something, since as I said the connection was successfully established, and the packet was successfully sent and received, if not by the sf::TcpSocket, at least by the server's computer.
:S