I heard that she supported intertextual marriage.
The four atheists who participate in Assisi are the French philosopher and psychoanalyst Julia Kristeva (who will speak before Benedict XVI)She might have called herself an atheist in the 1970s (though it might have been agnostic), but in 2007, she has published the book "Cet incroyable besoin de croire". ("That unbelievable need to believe"). I also saw newspaper articles and interviews where she makes it clear that she considers herself a member of the (Bulgarian) Orthodox Church.
What is "intertexual marriage"? She has developped the method of intertexuality in literary science. In fact, it also is surprising that she is credited as a "philosopher and psychoanalyst" and not as a literary scientist, although she is best known for the latter.
In fact, her life story is quite complex, she grew up both with Orthodoxy and the communist's atheist propaganda in Bulgaria, later came to France where she soon established herself in intellectual circles etc.
Under communism, people were taught to call themselves atheists. Stating in public that you're a believer could cause you quite some disadvantages. As for Kristeva, strangely enough, although the regime let her move to France, she continued to hang out with communist-minded intellectuals there. Only later, she started that she feels drawn by the Orthodox Liturgy, that she feels at home in church etc.
The point of her 2007 work is: She finds herself drawn to belief, but rationally, intellectually, she doesn't understand why she does. I would think that is what Saint Paul meant by "unto the Greeks foolishness".