Carcassonne is a world unto itself.
Vast but criss-crossed by streets and alleyways, protective but open-air, imposing but teeming like Occitania, the medieval city is like a maelstrom that takes you everywhere. As you wish, of course. Seen from above, its map resembles the board of a board game, with its monuments, stages and compulsory passages.
If you want to sample all the attractions, which is probably the case given that you've come a long way, you'll ideally need several days. Especially if you're a fan of good food and good wine, where time stands still while you chat with the angels, the motivation that brought so many of them here in the first place. And to come back.
Of course, if you're only here for a weekend, it's a different story. That said, to get the gist of it all, 2 days will suffice, as long as you've prepared well for your short stay and don't stay too long at the table!