In France, especially in the small towns, generally the only places open between 12 and 2pm - make that 12 and 2:30pm - make that 12 and 3 pm - are the restaurants, since all civilized folks go home for lunch. In addition to closing Sunday, the establishment will also close one other day of the week (ie, the day you arrive). In the large towns (Aumont-Aubrac, Cahors, Moissac, Condom, SJPP - generally the places marked in MMD with rail connections) the owners will often work out a staggered calendar (you close Mondays, I'll close Tuesdays) so that something will be open when you need it.
The eateries in rail stations are open whenever the stations themselves are open. You'll be coming from Paris - so stock up at home and pick up an extra sandwich at the Paris station.
If approaching a weekend, plan on stocking supplies on Friday/Saturday to last until Tuesday.