I don't know why you are sending 2 packets each time I call send
Not two sf::Packet, but two pieces of information, yes. The first one simply contains the size of the second one, which is the data itself.
Any script kiddie can crash the server
Of course. SFML is not a network engine, it's just a low-level library that provides tools to build your own stuff. If you want improved security, you must write more code.
Anything I can modify to ignore resent packets, or just not crash ?
Resent packets should work. Can you show me your code that produces the crash?