Not sure if this has been debated much, I just finished watching an episode and it got me thinking.
In “The Girl in the Fireplace”, written by current Doctor Who show-runner Steven Moffat, the Doctor appears to Renette at various times in her life, believed to be an imaginary friend until he appears to her again after she’s grown up some which of course I likened to Doctor 11’s introduction to Amy Pond. Then later when the Doctor mind melds (or whatever you call it) with her she comes to know him better than most because she is able to enter his memories when he enters hers.
Now, River claims to know the Doctor’s true name, going so far as to claim she knows him better than anyone in her first appearance in “Silence in the Library.” She (River) makes mention in the two parter “Time of Angels” and “Flesh and Stone” that while she and the Doctor keep meeting, they do so out of chronological order, something that the episode “Blink” and “The Girl in the Fireplace” show us is a one of those things that Steven Moffat likes to play with.
Finally, the cracks in time of 11th Doctors first season are connecting pieces of the universe that aren’t supposed to be connected, much like the time windows of “The Girl in the Fire Place”. The Doctor mentions in that episode and several episodes of the latest season that that sort of thing could destroy the universe.
Finally, at the end of the episode “The Girl in the Fireplace” though she dies, in the letter she leaves for the Doctor she says “reason says I shall not see you again but I have learned not to listen to reason.” The Doctor can’t cross his own timeline but we know he felt extreme guilt for not making it back to her, so perhaps by accident he returns to her before her death, like maybe the exact moment before she’s supposed to die. She was 43, just about the right age. He knows how to cure her. See where I’m going with this?
So perhaps, and of course I can’t possibly guess at the mechanics of it obviously, somehow Madam de Pompadour is River Song, through a combination of time windows (which is how she’s so future-tech savvy) and TARDIS travel. Just a thought.