Taxi at the Palace of Versailles?

I would still recommend using Uber. It's actually a great way to overcome the language barrier since you can enter your destination. We found it really helpful in Budapest, and it was so much cheaper than the taxis. I have Verizon, and I just pay a little extra for the month to have international data.

There are no taxi stands at Versailles. The closest taxi stand would be the train station, which is a 10 minute walk from the entrance.
There is a luxury hotel on the grounds, which might or might not have taxis available, but it's very close to the entrance, as well, so walking to the train station would be a better option.
http://waldorfastoria3.hilton.com/en/hotels/france/trianon-palace-versailles-a-waldorf-astoria-hotel-CDGTPWA/index.html

Uber is not allowed to pick up passengers at taxi stands at train stations or the airports, nor are they allowed to pick up passengers on the street. Regular Parisian taxis are allowed to do both.

I'm not sure that the luxury hotel would be the best option.

If you can agree to meet a taxi at a specific time and place, you would have to meet outside the grounds of Versailles.
If you want to arrange a pickup in English, you can do so in advance - either on the phone or online - with this reputable company (which is a regular Parisian taxi service). I would recommend calling and asking where the taxi could pick you up, before booking.
https://www.g7.fr/en/how-to-book-your-taxi-g7

Or, you might book a round-trip coach tour, which will take you to Versailles and back in air-conditioned comfort:
http://www.versaillesexpress.com/fr

Great info, thanks so much!