We arriving in France the day before Bastille Day and will need to get some provisions for our apartment stay in Avignon. Will there be any markets open where we can get simple provisions for a day? I assume that everything will be closed on the 14th?
Much depends on what time of day you arrive in Avignon on July 13. In Paris there are always little corner grocery shops, often owned by N.African immigrants, which stay open late in the evening, but if such are available in Avignon I can't say. Can you contact your apartment owner/agent and inquire?
I suggest doing a google search to see what's close by. If you arrive on the 13th there should be no problem. I recommend going to a supermarket as opposed to the corner places that sell overpriced soda and stale cookies. See if there's a Leader Price, Casino, Carrefour, 8à8, Marche-U, or even a Monoprix in the area.
Huit a Huit is a 7-Eleven type chain that is open during many non-traditional French store hours...even Sunday morning for a while. They are spread across southern France and carry fresh produce and provisions as well as a limited selection of other basics. If you can find one you should be able to get what you need on the Saturday you arrive.
The indoor farmers' market, Les Halles on Place Pie, is open daily until 1 p.m. It does not open Mondays which happens to be the national holiday this year anyhow. The central Monoprix, 24 rue de la Republic, includes a supermarket. It does not open Sundays and I can't sort out from this site http://alimentation.118000.fr/v_avignon_84/c_supermarche-et-hypermarche/e_monoprix-avignon_0490807790_C0051157395 whether it closes for the fete nationale.
Sorry, this is not a lot of help. Whoever represents the apartment should have better knowledge. Or you can try an e-mail to the city tourism office which in my experience is very helpful (and near that Monoprix) http://www.avignon-tourisme.com/home-1-2.html