I also have a cargo bike I use to get all sorts of things - from a full shopping cart to a large IKEA haul. Kids go in the trailer while the groceries are loaded in the cargo bike.
I live in Parisian suburbs and stores are all less than 10km away, I have never had trouble getting anything.
If I need something larger / heavier (say, cinder blocks and cement) I just rent a truck for two hours and get all the heavy shopping done in the time frame.