It's a long journey by train to Nice (5h+), so flying is a better option. Air France flies CDG-Nice, but I think it will be more expensive than your discount carriers. I guess it's too late to ask you why you didn't just buy a ticket with BA directly from London to Nice?

BA flies into terminal 2B. You will have to clear Customs & Immigration (not usually too long a line, maybe 5 minutes or so, but sometimes a 20-minute mess). Then you can take the new CDGVAL shuttle train to terminal 3. (I took this trip last week. I think it took me about 10 minutes to walk from the baggage pick-up area to CDGVAL (although this was from terminal 2D). A train was waiting, so we didn't have to wait. We took it all the way to T1 (T3 is an earlier stop), so it might be a 5-7 minute ride.

When and how can you check in for your Easyjet flight? If you can check in in advance and only have hand luggage, the connection should be possible if there are no delays out of LHR or landing at CDG. Ha - I forgot we were talking about LHR and a Friday night. I think the connection is risky, so you could lose the price of your ticket and have to find a place at the last minute to stay overnight. Depends on how much of a risktaker you are.