Chateau du Gandspette at Eperleques, and a vet in the village nearby. Lots of Brits use this site, for the convenience for ferries, but I doubt that the Vet opens at the weekend.
I think you have to have your dog done not less than 24 hours before sailing, but not more than 48 before, so the timing of your appointment is critical. If you don't fit this window at Calais, then perhaps better to have the dog seen nearer where you're setting off from rather than near the port.