For a few years now in France, we have been trying to use less plastic bags. In most of the grocery stores, there is a ban on plastic bags and therefore, nowadays, you have to pay to get a plastic bag/ or any kind of bag. The grocery stores are forcing the customers to bring their own "reusable shopping bag" instead of wasting lots and lots of plastic bags.
The process took a while, since customers didn't agree with the idea at first. But later on, they probably have realized that the use of resuable shopping bag was a good idea and great for the environment.
You can find reusable shopping/grocery bag in a lot of stores; for example I found mine at Marshalls for $0.99 ! (it is very cheap, so you have no excuse anymore. go buy one...tomorrow!)
Or make it yourself, like this one: (click on the picture)