I was able to take a few under strict "eyes only" conditions. There had been photo leaks a few days prior of someone who had bluffed through the security and sold photos to the press.

The press were going through the same day I was there, there are surely similar / better images that mine online.

Why is there an issue with photos of a public structure being released to the public? Have the rights to professional photos of Notre Dame been sold to a private entity a la the Eiffel Tower?

The rights to the Eiffel Tower have never been sold to a private entity, but the private entity that designed the night lighting kept their rights on it (which is the default, if the city didn't specifically ask for the rights to be transferred in the contract).

I don't think that's a good situation, but it has nothing to do with selling rights to a private entity.

I'm not sure I follow, to my understanding it is not legal to take professional photographs of the Eiffel tower at night, is that wrong?

Yes, because copyright remains with the original lighting designer and was never transferred - to or from - the public.