Hi, girlsmiley. The first day in, Monday, was maybe the second or third day the church was open to the public, and there was a 15 min line and a fair size crowd inside. I was able to sit and look around for awhile. It was about 9:30-10 AM. The second day I visited was Thursday at 8:30 AM with absolutely no line and few people inside. It was raining.
I was not aware of the roof being open. Perhaps I was not clued in? It was amazing enough to be able to walk in. It is very light and colorful now. I visited in the 70s and it was very dark and gloomy. From outside the church, one can see all the large cranes still in place as reconstruction is not complete. There are still a lot of metal supports for the walls outside.
I hope you enjoy your visit. PS, while I enjoyed visiting Notre Dame, just off the island near Shakespeare & Co. is a very small, very old church, Saint-Julien-le-Pauvre, where I happened upon one of the few services of the week. It was a highlight of my Paris trip. Best creche I saw.