We rented a Hyundai Tucson from Saint-Pierre-des-Corps train station (AVIS) near Tours in late Aug, and returned it in Carcassonne about two weeks later. (I didn't ask for a Hyundai Tucson, just an automatic - and was a little taken aback when I saw the size of this vehicle. The Tuscon was quite large for many of the narrow roads we traversed in SW France, and it already had a scratch and small dent on the passenger side from a previous renter. Despite my concerns, I added no additional scratches or dents. The vehicle was equipped (fortunately) with sensors on all sides. BTW, a few days later I rented a same-class vehicle from another AVIS, and was relieved when the make/model was physically smaller than the Tucson.)
There was a cargo cover, and the windows were lightly-tinted.
We left our luggage (under the cargo cover) in the vehicle at several stops, including a large city, and did not have a problem. One of the places we stopped matches one mentioned in your post: - during our drive from the Loire to Uzerche, we made a stop at Oradour-Sur-Glane.
Of course, we never opened the back of the vehicle (and thus did not expose our luggage) at any of the places we stopped.
One measure we took was to lock the handles of our two suitcases together when they were laying in the cargo space. That wouldn't have stopped someone from removing them, but it would have made it more challenging and more visible.