That's always been a hilarious part of French culture to me. Many of their cafes and sandwich shops are closed for lunch so their employees can go home to eat.
In what cafes and sandwich shop do you go to? I've never seen one that was closed during launch hours.
It's getting rarer but their is some that only open in launch hours instead of the whole afternoon, restaurant can have some specific services hours. (And some cafes stop serving drinks while serving food.)
French culture is to eat at specific hours, so it would be almost impossible to serve food only outside those.
Just small cafes around the park in Clermont-Ferrand. Strolling through the park at noon on a Saturday was the worst time to get hungry or need a drink.