plane train connection

Probably not going to happen. Where are you going? If on Air France, you may be able to book it just like an airplane connection, so if you miss it, they will get you on the next train without paying a penalty. Otherwise, it is not a good idea to book a train ticket separately, You're not even sure if your plane will land on time.

If you are considering catching a train that leaves 45 minutes after your flight is scheduled to land, don't do it. It could take you 15 minutes just to get off the plane once it arrives at the gate. Depending on the arrivals, clearing customs and immigration can be fast ... or not. Your flight will most likely arrive in terminal 2E and depending on which gate you arrive at, the walk to the station can be quite a distance. Bottom line is I wouldn't risk getting a train at CDG unless I had a minimum of 2 hours in which to clear customs/immigration, get to the rail platform and buy or validate my train ticket. And all of this is predicated on the fact you only have carry on luggage. Most likely you'll be in France for a number of days. Another hour or two at the airport won't destroy your vacation. After your long flight, take it easy, have a caffe and croissant, relax and start to enjoy your trip. After all, it is a vacation not a race.

I assume you are flying into France from the U.S. We've been on transatlantic flights that have been as much as two hours late arriving. There isn't anyway we'd try that close a connection with reserved or prepaid train tickets. We wouldn't even try that between domestic flight in an airport in the U.S. Better to have some extra time being bored than missing a connection.

You should leave at least 3 hours between ETA and a train at CDG and 4 hours for a train from Paris. 45 minutes is impossible; you are not likely to have cleared immigration in that time and planes are often late. The last 10 flights into Europe for us: 8 were late (one by 5 hours but that was unusual). Note even that much time is no guarantee; it is always risky to try to take a train or second plane after a cross Atlantic flight.

I usually count an hour from the plane's scheduled arrival to when I can walk out of the door of the terminal. And that's if the plane is on time. The only way you would ever make a train 45 minutes after your plane's scheduled arrival is if your plane happens to arrive an hour or two early.

I wouldn't classify it as completely impossible, if you have a carry-on only, but it's not something I would ever plan on. For me (with only my carry-on) I expect an hour to get to the RER B station in the terminal. If I make it sooner, it's a bonus. I haven't taken the TGV, but I expect it would take the same as RER.

As was said, you might take 20 minutes just to exit the plane. Customs and immigration depends on the line and whether they want a closer look at your stuff (I've had good luck there). I'd apply Murphy's Law and assume if you're in a hurry, they are more likely to be slow. If you had checked bags, including a gate check because your carry-on was too big, add another 30 minutes if everything goes well (why I never check bags). After that it's a large airport, and the people movers aren't particularly fast, so you have some travel time to get to the station and find your train.