Basel to Paris itinerary

Basel to Paris. There's a high speed TGV train for that specific route. Absolutely ZERO need for a car.

True, there is no need for a car, but need and want are two different things. Traffic on either A5 or A6 could make this drive a nightmare. Is this a day trip or are you planning to stop for a night on the way? If you really want to drop the car off outside of Paris, I suggest leaving it at Orly but I would drop it off in town at Gare de Lyon which is really quite easy to get to by car from the Boulevard Périphérique.

We took the TGV train from Paris to Basel last summer. It was so fast, and maximized our sightseeing days. Unless there's a certain sight along the way you are dying to see I would opt for the quicker route.

Basel to Paris is 3½ hours by TGV High Speed train, city centre to city centre. One train every 2 hours. Timetable is here: http://www.tgv-lyria.com/sites/default/files/pdf/BROCHURES_CO/TIMETABLE-2016-ch_fr-TGV-LYRIA-EN.pdf
By the time you crossed the border from Basel to St Louis (France), found the office and picked up the car, the train would be 1/3 of the way to Paris. And even when you got the car, it can't cruise at 300 Kph (188 Mph).

If you want to break the train trip with a stop, either for a few hours or overnight, there is:

• Dijon (on the train route, and some Basel - Paris trains stop there),
• Strasbourg ("normal" 200 Kph intercity from Basel), then direct TGV from Strasbourg to Paris.
• Colmar (between Basel and Strasbourg), then via Mulhouse or Strasbourg to get to Paris

Our hope is to see some vineyards in Burgundy. Might spend a night in Beaune and stop at wineries north of the city and then travel to Dijon.

renkenc,
Aha, so your plan was to spend a number of days and nights getting to Paris, it becomes clearer!

How about you take a train from Basel to Dijon, 3 trains per day, takes 1h24, as per the timetable I linked to above: http://www.tgv-lyria.com/sites/default/files/pdf/BROCHURES_CO/TIMETABLE-2016-ch_fr-TGV-LYRIA-EN.pdf
Then hire a car in Dijon, do your vineyard circuit, staying as many nights as you like, then return the car in Dijon, Beaune or anywhere else you like and take a fast train to Paris.
Gives you your touring, but no long Autoroute drives just to get from A to B.

I found some maps of the Burgundy wine region,
here: http://www.pcommswines.com/wp-content/uploads/2009/06/la-bourgogne-map.jpg
and here: http://winefolly.com/wp-content/uploads/2014/01/Burgundy-Wine-Map-wine-folly.jpg
As you can see Dijon is conveniently at the northern end of the area.

Thanks, good suggestion.

You should also seriously consider visiting the Alsace area near Basel, esp. Colmar, Riquewihr and surrounding communities which you can visit either by car or public transportation, although a car allows more flexibility for the surrounding rural areas.