You have a FZS1000,the carbed version, known on here as a gen1, 2000 to 2005 but with some late registered 2006 ones about.
An FZ1 is the later bike with fuel injection , known on here as a gen2, 2005 onwards.
Confusingly the model you have is known in America as a FZ1, be careful when buying stuff on ebay.
Your fairing lowers are aftermarket but top looks original, the bike looks like an import as the orange reflectors on the forks are not on UK models, which would explain the FZ1 stickers.