airport transfer CDG to Paris?

With 2 large pieces of luggage the "best" is a taxi which you have no doubt suspected.

Second vote for taking a taxi.

Unfortunately, it will be a challenge to travel via public transportation, if you'll be lugging around "two large suitcases"

Is it too late to reconsider your packing?

A simple Google search will show you the flat rates for taxis ex CdG into central Paris. Be sure to use the official taxi queue.

In the daytime it's either 50 or 55 Euro into central Paris. Late evening or very early morning costs more. Pay for a taxi here and you will feel brilliant and pampered. I'm a cheapskate, but have started taking taxis between Paris and CDG. It's too hard for me in my advanced years to move myself and luggage around via public transportation. You can be in a taxi 30-60 min. after landing, depending on various factors, of course.

Are you sure that it costs more to go to or from the airport in the evening?
I thought the flat rates were in effect 24/7.

Flat fee is at any time. The choice to lug large suitcases is the choice to use a taxi.

Why do you have 2 large suitcases?

A good tip in advance of travelling is to lay out everything you are going to pack and take half of the stuff away. Remember too the absence of elevators in many buildings in Paris.

There are always a number of free luggage carts at CDG, which would probably be much easier than hauling two separate large suitcases.

But you would have a problem getting two big suitcases on a bus, and the Metro would be impossible due to the large number of stairs.

Depending on where you need to go in Paris, the RoissyBus might be a consideration. http://www.francetravelplanner.com/go/paris/trans/air/roissybus.html

I agree that either a taxi or private transfer is the way to go. There is much to be said for door to door service. We used this one last time we went and were very satisfied with the service.

http://www.interserviceprestige.com/rates.php

I have scheduled transfers from Paris airports through Viator. It's about $22. You just call them when you arrive, and they pick you up in a van and drop you at your hotel. Great, inexpensive option.

The advantage of a private transfer for you is this: when you emerge with your two large suitcases a driver will be holding a placard with your name on it. (S)he will take your suitcases from you and you can follow him to the vehicle. Otherwise you need to schlep your bags to the taxi stand.

When you have already schlepped your luggage through long corridors and on escalators in at least 2 airport terminals, it hardly seems worth it to pay someone a lot of extra money to walk your luggage a short distance to his car.

The taxi stands are located just behind the guys holding the signs with your name on it. Don't let yourself be taken by this racket - if you have made it this far, a few more feet won't hurt, and will cost you just the flat fee into Paris.