It has been a few years since we went over on foot. However there are regular buses run by the ferry companies into the town centre. They were free last time I went but that was a few years back. The big hypermarkets are on the outskirts of town and you will need a bus or taxi to get to them. There are smaller supermarkets in the town. There is one on the far side of the market square. These will be cheaper than at home but probably not as cheap or with as large a selection than the hypers. There is an Auchan at Coquelles which is on a bus route. I don't know if buses go to the Cite de Europe. The Auchan has other shops and cafes and there is a large wine warehouse in the same complex. However you are limited by what you can carry.

Must admit I don't go to Calais for the culture but there is a very good war museum in the park opposite the town hall. There are several nice restaurants which I assume will be open at this time.

Hope you enjoy the visit.