It isn't!
What you are seeing is stone vaulting, essentially a great big three-dimensional arch, related to a hemispherical dome in somewhat the same way as a gothic arch is related to a Romanesque rounded arch. It may or may not be painted or plastered or frescoed (ND's wasn't, I think) but the actual "ceiling" of the church—and, crucially, the structural part of what's over your head—was/is stone. The roof in a modern building is often structurally keeping the tops of the walls at a fixed distance as well as holding itself up, but in a stone cathedral, the roof was an extra layer over the top of the stonework, primarily to shed rainwater.
All of which is to say, the loss of the wooden roof structure is a lot less threatening than the loss of (some of) the vaulting; and replacing the roof with glass or stained glass would be utterly invisible from inside the church, whose ceiling would still be the stone vaulting.