TER or taxi to CDG?

Taxis are a standard rate of 55 euros from central Paris to CDG so for convenience would recommend rather than take the RER.

You can book taxis online, G7 are pretty good - have used thses before

https://www.g7.fr/en/

Taxi would be 50€ from the Right Bank and 55€ from the Left Bank plus either the 4€ (immediate dispatch) or 7€ (pre-arranged) dispatch charge. In your situation, I would take a taxi unless I was I could manage 3 pieces of luggage very easily and would not have to make a connection to catch the RER. If you are traveling in economy, arrive 3 hours before scheduled departure. You can push that a bit if you in business class and arrive between 2 and 2.5 hours before departure time. If you have VAT refunds to do, add an hour to those times to allow time for that process. Usually, that takes less than 20 minutes but I have waited in line for almost an hour there.

It's not the TER, its the RER (Paris Express Commuter Network).
"2 carry-ons and a bag to be checked?" - There are no checked bags on trains, you have to carry all your bags yourself. If you have more than 1 bag per person a taxi may be the best idea.
"I assume I should arrive at the airport 2.5 to 3 hours early, is that correct?" - Depends where you are going and which airline. You need to check with your airline to find out. This should be on their website.

These days, with extra special security for flights to the USA, 3 hours out of CDG should be a minimum.

What does Air France advise for airport arrival time before flight?

Based on what I have read on this forum, I would be at CDG no later than 930, especially where you have luggage to check

"There are no checked bags on trains, you have to carry all your bags yourself. " I think the OP is referring to a bag that will have to be checked for the flight as opposed to checked on the train.

I would take a taxi - directly to your door, no hassle with the TER and luggage.
I'd suggest 3.5 hours to arrive at the airport.

I'd definitely allot at least 3 hours at CDG. There's a large bank of westbound flights to North America at this time and so the terminal tends to be very busy in the mid- and late morning. In addition, since you will be departing the Schengen zone you need to proceed through exit passport control, which can sometimes be time-consuming.