Good day!
We're ending our trip with a few days in the Loire region probably in Blois or Tours. We are renting a car and have to drive back to Paris Beauvais airport on September 3rd 2024. My wife especially would like to avoid having to drive through Paris on the way to Beauvais. What route can you recommend we take from Tours/Blois to Paris Beauvais Airport to avoid driving IN Paris.

Thank you!

check in your car and catch the train.

Have you tried the route tool at www.viamichelin.com ? It shows itineraries that do not pass through Paris.

You never have to drive through a city. All major cities have "rocades" (orbital roads). Paris has 3 of them, périphérique, A86 and A104. Be prepared for heavy traffic for all of them even outside rush hour.
If you want to follow Bilbo's advice, train to Montparnasse, metro to Porte Maillot and bus to Beauvais airport. I haven't tried this bus for a long time but when I did, it was very well organized. I think that your final destination was even displayed on the bus at Porte Maillot.

PS: I see that you plan to go to Beauvais when the paralympic games are still on. Maybe a good idea to stay as far from Paris as possible. As advised by Kerouac, use a search tool and add an intermediate point west of Paris.

No reasonable driving route to Beauvais from those places would go through Paris.