So AA flights land T3 LHR (well, PHL does), while BA to CDG departs T5 LHR.
Without baggage following the purple signs to connections is easy, but it'll take longer than a same-terminal transit.
If you decide to drop a bag then you're in a different situation: you'd need to collect from T5, meaning you'd need to enter the UK. You can't then transfer internally, you'd have to get T5 to T3, which is possible by tube or taxi or Express train, but it's all time time time (and money in some cases).
General advice on connecting nested PNRs is to ensure a very minimum of 3hrs. You very well may not need that at all, but if I do similar nesting I'd bake in 4hrs minimum.
If your CDG-LHR is late and you miss LHR-PHL then that's on you, the airline isn't obligated to put you on the next flight for free (it can happen, though).