There's not one within walking distance of the ferry terminal.
It's roughly a 15 minute walk into the town centre or you can take the bus that meets the ferries. (I can't remember the exact fare but it's not expensive at only a euro or two).
I usually walk into town (when I'm not carrying very much) but take the bus back (when I'm laden down with bottles of plonk).
In the town centre you'll find a large Carrefour, which probably stocks everything you might want anyway. (There's also a much smaller 'Express' branch of Carrefour close to Calais Ville rail station. That's where I usually buy my wine because it's very close to where the bus back to the ferry terminal departs from, making it easier to carry everything).
There's a handy free bus service ("Balad’in") which runs across the town centre every 10 minutes.
Most of the hypermarkets aren't easily accessible by public transport but, once you're in the town centre, you can take a Line 1 bus to Cité Europe, which is a major shopping mall (somewhat similar to Lakeside or Bluewater in the UK), where you'll find a very large Carrefour.
Free bus route:
http://www.sitac-calais-opale-bus.fr/images/Baladin/PlanBaladinHiver2013.png
Main bus routes:
https://www.calais-cotedopale.co.uk/sites/calais-cotedopale/files/content/files/plan_reseau_calais_hiver2016-17-semaine_0.png
Cité Europe website:
https://www.citeeurope.com/