Dan Brown is a genius troll.
Consider that: he studied art history, so he can't possibly fail basic knowledge of it.
Jacques Chirac was somehow involved in the movie's production (he, amongst other things, wanted Sophie Marseau, his daughter's friend, to play something there) and at least five of his ministers were freemasons - it's pretty likely that he's a mason as well (Mitteran being a mason in the book is likely a reference). The book has that general idea of marginalization of the church, which is what masons would very much adore. So there just might be quite some mason money involved in the book, and certainly in the movie.
Dan Brown himself is more of a Christian than a mason.
a) Everyone remembers the ending, right? The main antichristian in the book is suddenly the main evil guy as well.
b) There's so many blatant errors obvious for everyone who's a little bit intellectual, enough for them to disregard the theory altogether.
TL;DR: Brown took masons' money and wrote a book that mocks them.