Rental car size

Sorry, I have no idea about the roads but wanted to point out that compact cars, even if they don't have GPS, should have some kind of CarPlay system so you can use the GPS on your phone, like Google maps. I did that in Germany and had no problems at all.

If you have a smartphone, you don't need a GPS.
You can use Waze, Google Maps, iMaps, or whatever.
And in most cars they can be connected CarPlay.

I drove all over France with a mid size car and never had any problem with the roads being too narrow or not well maintained. That included Provence, Normandy, Brittany, Alsace, parts of Burgundy and Loire Valley. Car was very new with Gps and great fuel efficiency. You should have no problem with a mid size.

A midsize car is fine for the roads.

Use Google Offline Maps: Download the map area (or areas) you are interested in over wifi before leaving on your trip. You will then be able to use Google Maps for directions without a cell phone plan/signal.

Roads aren't particularly small/narrow in Burgundy. No issue at all!

With the high fuel prices these days I would look to fuel economy too, yet powerful enough to drive uphill easily if needed.

I lived in Bourgogne for several years. In some medieval towns, you may feel as if you need to pull your side mirrors in to avoid damage on some tight passages, but you shouldn't have any serious issues. I recall one where it seemed as if my wheels were scraping the curbs and I felt that road probably should be posted with a warning, but you should be fine. What kind of car do you mean when you say "midsize?" Something like a Renault Mégane?

Parking spaces seem to be scarce so smaller cars are preferable. Park as close to curb as possible and fold your side mirrors in, especially in smaller towns with smaller roads. Roads outside towns weren’t a problem but they often have minimal or no shoulders, depends on your area although trucks and buses often had me mentally trying to shrink my car.

I've found that despite not being listed, compact cars we have rented do have GPS.