When are the restaurants closed?

Many French restaurants close on Sundays. Some also close on Mondays, including some of those that are open on Sundays. A few places that are very oriented towards the business lunch market will only open in the evening on Friday and Saturday.

Yes, it is true in France and many other countries. The day of the week varies from restaurant to restaurant, but the opening times are posted outside the restaurant. Sunday and Monday are the most common "Ruhetag" (as it is called in German speaking areas) as they are the least popular nights. But there is often one place in town with a different "Ruhetag".
They do this so the staff (and owners) can have one day off per week. Otherwise they need two cooks, two sets of kitchen staff and more waiters to cover 7 days, not economic for small places when Monday is "quiet" anyway.

Yes in Italy, the day of week does change more from town to town. Last year, I hit pretty much every stop on a limited-selection day, but the towns were not so small for it to be a problem. This info is not usually at the start of Rick's chapters, but you'll discern a pattern within the restaurant listings themselves. I think France is more consistent.

Unless you are in a very small village, you shouldn't have a problem finding a restaurant or cafe open on Sunday and Monday evenings. Your B&B host or hotel staff will be able to provide information about local restaurants. I have done three road trips in France covering a total of 11+ weeks and I don't remember ever not being able to find a place open for dinner. Now, finding open shops from noon til 2pm can be a problem, especially in small towns, so be sure to pick up your lunch picnic supplies early.

My experience is limited to late June last year in Burgundy and Alsace. In the very small villages, a lot (both shops and restaurants) was closed on Monday and some restaurants only opened for lunch and dinner from Wednesday or Thursday through Sunday. So I went without lunch once in Burgundy. I spent 3 nights in a very small Alsacian village and at least one restaurant was open every night (though I wasn't there on a Monday) and I could easily have driven less than 1/2 hour to Colmar for dinner.

Restaurants are closed when they are not open. :-)

I have never found it difficult to find somewhere to eat no matter what day or what country. Some of the higher end restaurants, which I probably would not have eaten at anyway, are closed Sundays. I have always found plenty of other options open and available and I don't mean just fast food.

My comments deal with the opening of the restaurants in France. At dinner here the restaurants open at 5 pm , 5:30 pm or even 6 pm. Don't be surprised if some French restaurants don't open until 7 pm. What you miss is an early dinner.

Yes, we understand that restaurants open much later there than here. As Rick says, go at 7:30 and you see the restaurant full of tourists; go at 9:30 and restaurants will be filled with locals! Our funniest experience was in Italy the day the time changed back to Standard time. We were unaware, since it was before smart phones, and went to a restaurant at 7:30 only to find a few of the staff sitting out front reading the paper and enjoying a cigarette. They obviously turned us away to return in a couple hours! :)
But yes, we went a few nights on a sandwich or leftovers from a picnic because we were unaware that we were looking for a restaurant on a night when nearly all of them were closed. It's always best to ask the host when you arrive which night that is, and plan accordingly.

Philip's response gives you the information you need.