You won't actually be going anywhere near the FCC, which is the T1/T2 connections facility.

You will be arriving at T3, where you follow signs to T4 connections, as BA's flights to CDG leave from T4. See here.

It is VERY unlikely you will get on an earlier flight, unless either (a) you have a fully flexible ticket or (b) your flight is oversold and they are looking to move people off the flight onto other flights.

Of course it is worth asking at the ticket desk on the way, but very very unlikely, without paying the change fee on your ticket and the upgrade to the lowest fare available (which may well be the full fare).