It is a general principle of the law of England and Wales that anyone may bring a prosecution for any criminal offence. Legislation contains some limited exceptions to this general principle, but I cannot find any exceptions relating to national-rail ticketing offences. So, as
ainsworth74 suggests, there is nothing to stop FCC proceeding with a prosecution. Equally, in principle there would appear to be nothing to stop the new franchisee prosecuting instead. I say "in principle" because I haven't checked whether transfer of the information relating to a particular case would be permitted by data protection legislation.
Why would Great Western have anything to do with it?
I imagine that the OP looked at the scaled-down FCC website and saw the invitation to use FGW, as a sister First Group company, for future ticket purchases.