Looks like the answer is “some”. We’re here in Paris now and, speaking to some restaurants, shopkeepers & neighbors, it appears to be uneven. We have reservations at Fulgurances, a restaurant I would’ve expected to be closed but isnt. Our corner wine store guy also plans to be open, but the bakery across the street is going to be closed.
Some supermarkets open in the morning on bank holidays. I'd expect Paris to be more liberal in terms of what's opening than the back of beyond where I live (yes, local supermarket is open tomorrow morning). And there's always a boulangerie open somewhere.