How do the Europeans shop? Do they get plastic bags at the markets or do they carry bags to the shops and stores? How do they carry the bread home from the shops? We are going through a change in the states. It would be nice to know how other people around the world get their food home.
It is impossible to answer such a general question about Europeans. Even within the European Union we have 27 countries and, of course, there are other nations not within the EU. Perhaps surprisingly to the OP, we all have our national traits and different ways of doing things, including shopping for food.
I can answer the OP's questions about the UK:
How do we shop? Most of us shop in supermarkets most of the time.
Bags? Supermarkets issue plastic bags. Some charge for them, others are free. Most also sell heavy duty plastic bags - which they will replace when it wears out for free. My normal supermarket calls these "bags for life". Some people have their own bags. We are individuals, there isnt a common way of bagging purchases.
How do we carry bread home? In the bags, of course.
Plastic bags are no longer distributed for free at large supermarkets in France, but I don't know if this has really led to a significant increase in awareness or bag-reuse. I think a lot of people have just gotten into the habit of buying one or two bags at the check-out every time, because they cost next to nothing. Either that, or they grab those flimsy bags from the produce section, which are still freely available. I usually show up with an empty backpack, and depending on the neighborhood and how shady I'm looking that day, the security guard might not even let me into the store with it. Frustrating.
Deppity, I see most people carrying their own bags in my part of France -- most women carry one or two small foldable bags in their handbags (including me) for small trips, with the big bags coming out for the long list trips.
But I sure don't see many empty plastic bags floating around (unlike on a recent trip to Florida).
It depends where in Europe you are and what regulations/laws have come in recently. In Malta for example you cannot get a traditional plastic bag at the checkout, you have to either have your own bag(s) or purchase one of their non-plastic bags.
Some places in central Europe where I currently live charge for the traditional plastic bags as well as selling the non-plastic reusable variety. I've noticed a huge drop off in the use of traditional plastic bags where they are now charging for them, even if it is a small monetary amount. There are far more people who shop with their own bags whether those are backpacks, reusable bags, beach bags, or the otld school two wheeled shopping bag/cart. I've also noticed people (me included) who load everything back into the store supplied shopping cart, wheel it out to the car, load the trunk, return the cart and then drive home. I do this because I often forget the reusable bags in the car to begin with.
But, I am generalizing on the small piece of Europe I have exposure to (Czech, Austria, Slovak, etc...) I'm certain other practices exist and hopefully others, in other countries will chime in.