Terri, ignore customs (check on goods), it is a non-event. It is a random stop only, 95%+ are not stopped, you just walk through and it takes zero time.
What takes time is immigration (aka passport control). This is the check on people, whether you are allowed into the country and for how long. This could take 30 to 90 minutes, with occasional horror stories of it taking longer.
Immigration will take place when you land at Charles de Gaulle. It makes no difference what your onward travel method is (fly, train or other).
Plus, a transatlantic flight could be 1 hour late if the wind is in the wrong direction. The normal wisdom is to allow 3 hours minimum, plus and check-in time if you are flying. Therefore earliest flight out would be 12:00.
If you do this as a separate booking, you are taking the risk. If or any reason you miss the onward flight, you have no come-back or refund.
You could also take the train. That would involve first a train into Paris, then the métro and a train to Nice from Gare de Lyon. Total 7 hours minimum, so the earliest you would be in Nice is 19:00.
https://www.bahn.com/en/view/index.shtml