I don't have console controllers to know what's going on for sure, but PC controllers tend to work a lot better at this. I have an old Logitech Gamepad and its plug and play, but like Kaldarasha said, I still have to start a New Game and go into the Menu -> Config screen to change my control scheme to what I prefer. If the game doesn't recognize console controllers at all (I'd understand since we're talking about a 1998 game working with much newer console controllers), then using programs like JoyToKey and Xpadder to map them to your keyboard should be the next step. You still need to go to Menu -> Config after starting a New Game and adjust it to your liking.
There are mods to change the controller icons ingame that match the Playstation and Xbox buttons, so it's being done already by others. Use the search tool and look around for your answers.