First question: seen the pattern, especially the ventral red and black part of opisthosoma, I thought to what was former called Hogna narbonensis, and that as far as I know was latter defined Lycosa narbonensis and now should be included in Lycosa tarantula. So I'll see the confirms or remarks also to see the opinions on taxonomy.
INaturalist turns on this species if I type L. narbonensis.
About this species in southern France, you can see this page: https://www.insecte.org/forum/viewtopic.php?f=42&t=125817&hilit=119452

Nice discovery: sat down on the ground, I saw some ants feeding on the corpse of a specimen,of which I've taken afterwards some photos at home. Then, I saw that the holes in the ground, that I thought could be of some mice, were instead occupied by some spiders. Six burrows in four meters of distance, with three specimen (plus the dead one) seen in their holes. And an exuvia of a male.
About 22 mm. body lenght (or something more, it was dead and dehydrated.

In the photos: the dead spider (with ventral view and epigyne); the exuvia (with male palp); one burrow dimensions (no silk seen in it, on its edge there were just some short leaves of grass arranged and fitted around); two spiders who gave a look out of their burrow, and the abdomen of another one remaining in the shade.

https://araneae.nmbe.ch/gallery/photos/3977