The gear for the virtual reality experience for Notre Dame is housed in a backpack that is linked to the substantial headpiece that you wear.
In other words, you are wearing a computer on your back that feeds the goggles and earphones in order to create the virtual experience.
You can’t see anything real around you — you can only see the virtual reality that they have surrounded you with.
And indeed, the "virtuality" of the experience is so real that you do feel you could fall off a parapet, or that you are zipping up in the sky. Of course the Notre Dame experience is meant to take you from ground level up to the tops of the towers and within the roof, whereas presumably Nadar's exhibition space (which the Impressionism exhibit is replicating) was presumably only on one level - or at the most, two. However, it could be that the virtual Impressionism exhibit also takes you on some kind of bird's-eye view of various Impressionist paintings -- but from what I read about it, I understood it was to walk you through what it would have been like to walk through the exhibition.
P.s. for the second part of your question, as to how you walk around, the virtual experience also marks out virtual "boundaries" if you are getting to close to a wall, and other people show up virtually too in a different way than the virtual characters. You can literally walk through your virtual host, for example, but if a real person is next to you, you will see their outline so you know not to run into them.
If you go to the Notre Dame experience official website and scroll almost to the bottom page, they have a video trailer - in that, you can see a brief — VERY brief — couple of shots that show visitors wearing the gear
https://www.eternellenotredame.com/en/
And if you go to the 34-second mark of the following video, you will see what is really happening — people walking around a low-ceilinged room with the computer on their back and headset !!
https://www.francetvinfo.fr/culture/patrimoine/histoire/eternelle-notre-dame-l-experience-immersive-inedite-pour-decouvrir-l-histoire-de-la-cathedrale-du-moyen-age-a-nos-jours_4915375.html
(You can also see in that video a computerized human form, “Ludovic,” which shows what a physical person next to you looks like, and at about 1:40 in the video, you can see people walking along “climbing” over an obstacle!)
Both videos also give an idea of what it’s like walking on the edge, looking down, getting whisked up to the towers, etc.
The videos give a sense of how realistic the experience is, but they don’t show how you literally can look around to 360 degrees all around you, and the experience is completely detailed all around — up to the highest skies, behind you, in front of you . . It’s truly mind-boggling at least in the case of the Notre Dame VR exhibit.