I don't know how reliable this is after so many years of my emailing and Facebook messaging them with no reply, but I finally got a reply from Robért Fresh Market:
"You can expect a new site and online shopping platform very soon. Thank you."
One can hope! :)
I doubt very much that I am the only person in this city that is embarrassed by how truly behind New Orleans is regarding the ability to order groceries online and have them delivered. I suppose the Walmart pick up thing is somewhat of a start but I doubt I'd actually use Walmart for groceries but at least they have lists, which is more than I can say for any of these other services. Instacart, Peapod, Shipt, heck, aliens from space, please come here to New Orleans and give us an efficient online grocery shopping and delivery service! :)