https://www.videogameschronicle.com/features/interviews/interview-the-real-story-behind-goldeneye-hd-as-told-by-its-directors/ said:
So the remaster ran on the original code?
ME: Yeah, so we took the original code and then Laurie [Cheers] began converting it chunk by chunk, He got the basic game loop running on the Xbox, then he moved on to drawing the characters and other stuff, changing as little as possible.
I think it was C code on the Nintendo 64 and C++ on Xbox. We were keeping all of the code the same, so when you were walking around the game the collisions were exactly the same on both versions. That basically meant we had to keep the same graphics so that the collisions would be the same and things like that.
It was enjoyable to see it slowly come back to life, with Laurie starting with this small core and slowly adding bits on as they were converted. It was pretty cool.