Travel from Basel, Switzerland to Paris, France DeGaulle Airport

Well, you could fly there.
By train, TGV to Gare de Lyon, RER A to Les Halles or RER D to Gare du Nord, RER B to Charles De Gaulle.

I wouldn't try this on the same day as a flight out of CDG, unless you are feeling VERY lucky. If there's any disruption, you could easily miss your plane.

Unfortunately the budget air carriers don't fly this route--just Air France.

As above, train or plane.
Train should be reliable and on time. You either get a train direct to Paris Gare du Lyon, then RER (change once) to Charles de Gaulle.
There are a few trains where you can change at Strasbourg and avoid crossing Paris, for example:

Basel SBB depart 07:51, Strasbourg Ville arrive 09:09
Strasbourg Ville depart 09:46, Aéroport Charles-de-Gaulle TGV arrive 12:17

As you see, unless you have an flight after about 14:15, you will have to travel the night before and stay overnight at the airport.

You can fly, but the saftety margin you will have to allow for two unconnected flights makes that not much faster.
The budget air carriers gave up on the Basel - Paris route when the introduced the TGV's.

And to me two hours from arrival at CDG train station before your flight is NOT really enough if you're flying out internationally. You will still have to make your way to your terminal. If you're flying out of Terminal 2E, ok, that's easy, but if your flight is out of Terminal 1, for example, you still have a good additional 20 minutes to get to your terminal before you can get in line to check in. I would say don't try for that train combo that arrives in at 12:17 unless your flight departs at 3:15 or later. But that's my own assessment based on my knowledge of CDG and personal risk appetite. (Of course you need less time if you're catching another intra-European flight.)

And pray that you fly on one of the 10 days out of the year that the French are not striking over "something"...