No, we do not work during august. We are all on strike, supermarkets are closed and we are all starving to death. That's why the population is halved every year.

who is working at restaurants and stores?

Literally your own post

Like every country where corporations don't run the government. There are less service industry workers available during the peak summer months as they go on vacation like normal people. The whole country isn't closed though, you just have to be patient and be pleased they have that right to do so - it's a sign of a people-focused economy.

Go to Italy and see some people who are doing it for real.

The French are rookies :)

Have you considered posing the questions like this first rather than assuming the odd thing is true, and asking why?

Maybe ask if the thing you're assuming is even true to begin with?

There is not strict rules for days off in France.

It depends mostly of your work. Some work will force you to put your days off in the summer but that's not super common. Most jobs just let you use your days off however you want.

And no it's not a misunderstanding, some employers actually don't want their staff to work in the summer because all businesses slow down and people are in vacations.

Basically it mostly depends of your line of work but most people are free to choose when they take their days off. They just happen to often take them in the summer. That way if they have kids they can spend time with them while they are on summer break.

Some others will on the contrary put their days outside of the school holidays because travelling and tourism is cheaper when most people are expected to be working.

Basically a lot of it depends if you have kids and when their holidays are. Each region of france has different schedule for school holidays. So it somehow guides a lot of the days off placed by workers.

Also do waiters eat after lunch and dinner service? or do they shove their faces quickly during meal service?

I'm not sure but usually it seemed to me like they tend to eat after service but really it all depends of the manager of the restaurant.