TGV Lyria vs. SNCF - Basel SBB to Paris

Is there any great advantage in using TGV? It's a bit faster, but not much.

In this case I would say no. you can use the $100 to pay bills and offset the unfavorable exchange rate; You can see pictures and read about the amenities available on French trains on this
https://www.seat61.com/France-trains.htm

I believe you will be on a TGV, from Strasbourg to Paris. The Basel-Strasbourg train is most likely a TER, a French regional train without seat reservations, but perfectly comfortable. And you will arrive at a different station in Paris, Gare de l'Est.

How are you obtaining prices in dollars?

When booking trains, avoid Raileurope. Look at Trainline, Loco2, or directly at the SNCF website.

When you are traveling is important as rolling strikes have disrupted travel within France. If you travel on a strike day, itineraries with multiple connections can be very problematic. I might also suggest that you purchase tickets as soon as possible as prices generally only rise.

TGV's are a type of train (=Train à Grande Vitesse = High Speed Train). They are run by SNCF, which is a company (= Société nationale des chemins de fer français = French National Railway Company)
Both routes will involve a TGV run by SNCF.

Basel to Paris direct = one train, a TGV to Paris Gare de Lyon
Basel - Strasbourg - Paris = 2 trains, TER to Strasbourg and then TGV to Paris Gare de l'Est. A TER is "medium fast" (200 Km/Hr). This is a longer route and takes more time.

Yes, there are some bargains available on the Strasbourg route, if you are prepared to sacrifice time for money.
I would double-check prices on https://www.trainline.eu/ or the SNCF website.

How much luggage are you carrying -- and how much are you willing to pay to avoid off-loading it, hauling it across the station and getting it on train #2? Also, does the Paris destination station make a difference based on where your hotel is located?

Tocard: How are you obtaining prices in dollars?
- I'm looking on trainline and seeing prices in dollars, although the payment is in Euros
- As far as strikes - yeah they make me nervous! RichSteves says "don't sweat it", but you've got me thinking that maybe the direct route may be a safer way to go... We would be traveling mid-August.

Chris F: Thanks so much for the detail. I had wondered what some of the abbrevations stood for and hadn't taken the time to look it up!

Laura B: How much luggage?! Good question! We want to keep it as mininal as possible and keep it with us. We'll be traveling to Basel from Wengen and that will take 3 or 4 trains, so we need to travel light!

Followup question: Some connections are tight - 5mins, 8mins and the like. Should I be worried, or do these trains really run reliably to these tight schedules?!

8 minute connections at a big stations can be tight. If arriving on a regional train, they can be a minute of two late, and then it is really tight. They often will not hold a TGV for a regional train connection, but they might hold a regional train for a late arriving TGV. When you are late arriving on a regional train, you can get new reservations on the next TGV, but it could be a 2 hour wait. Its just like airline connections.