I'm sure I've photographed TGVs at Calais Ville, presumably an extension of the same workings.
Mind you, I haven't been over to Calais since 1st October 2000*, only through it!
*When the hovercraft ceased running.
IIRC, there's also a handful of TGVs from Calais-Ville through to Paris-Nord (as well as the Eurostar, which is classed as such domestically, and needs ID to travel on).
Your mention of hovercraft has also reminded me of the wonderfully named (and very 60s-futuristic) station further down the line, of Boulogne-Aéroglisseur, now also gone.
My main memory of Calais-Maritime is of catching old Corail sets down to Amiens (where I lived) from the boat-train tracks that came almost to the ferry itself (with very little station left at that point), having previously 'enjoyed' the buffet at the by then roofless Dover Western Docks.
As a further note on access at Calais - the free bus is no more, but there is a local, paid, bus route that goes to the port, and it's really only an 8-10 minute walk from the port to the town (and another 5 on to Calais-Ville) if you want to stretch your legs.
From Calais, as well as links to Lille and Paris, you can get down the coast, to some of the old-school resorts (Le Touquet in particular) and through to Picardy - Abbeville and the impressive cathedral, floating allotments and old town of Amiens. Inland, and you can head to Arras, capital of the Artois, with a more Flemish than French feel to it, via the bleak industrial towns of the north (their slag heaps now used as dry ski slopes). You can also head along to Dunkirk, although the connection across the coast to Belgium, and the Kusttram to Oostende and points beyond, is now gone.