As I understand his thought, d'Espagnat argues from the non-localisation of objects associated with a quantum mechanical understanding of them to the notion that the whole of reality has being "as a whole" and that "being" should not be associated with any individual object in isolation from others. He argues that the (mathematical) formulations of quantum mechanics represent a tool that can be used to predict the outcomes of measurements that we might make of events, and resists the giving of any "reality" to the wavefunctions and their associated probabilities of differing outcomes. Thus, at a superficial glance, his thought can appear to be idealistic - in the philosophical sense of that word.
However, d'Espagnat does talk about "Being", with a capital letter, as being a kind of ground behind the phenomna of quantum mechanics. In my own way of expressing it, d'Espagnat recognises that quantum mechanics, because of its probabilistic and non-localised nature, moves the question of existence away from being just a question about the existence of old-fashioned, physical objects that we can touch, feel, throw around and measure with a metre rule to being a question about what it existence is in itself. The philosophical implication of quantum mechanics is to force us to think about the idea of Being, and, for d'Espagnat, this consists of some sort of "Being" that takes in the "whole" of what is contained in the quantum mechanical formulation of things.
The idea of God to which d'Espagnat is attracted is that expressed in the way God reveals his name to Moses: "I am who am". He is in some ways more attracted to Eastern religions, with their sense of mystery about existing/being, than he is to Christian faith which has a "harder" tradition of the way it understands being. So far as I can gather, he is agnostic so far as the existence of God is concerned.
The most accessible account of his thought I have been able to find is in the text of a lecture or paper on the website of the Pontifical Lateran University: "State of the Art" and perspectives: Quantum Physics and the Ontological Problem. There is also a shorter account in Bernard d'Espagnat's statement on receiving the Templeton Prize.
d'Espagnat's work does raise a question about the ability of mankind, whether it be through the methods of science or those of philosophical enquiry in the broadest sense of that term, to come to knowledge of the Reality that he describes as being "veiled". If this "veiled" is understood in a Balthasarian sense (and there is no reason to think that d'Espagnat explicitly does understand it in this sense), it is at once a "hiding" and a "showing" that can reveal to us Reality. One can perhaps imply this possibility in d'Espagnat's thought. At the end of his paper from the Lateran University, he writes:
..it seems to me that there is some relationship between the "ontological suggestions" of contemporary physics and the "negative theology". My point is that there exists a similarity between the notion of Mind-Independent Reality - so much removed from our way of thinking that is is not even embedded in space and time - and the God of this theology, concerning which we can say what it is not. Consequently, I would not be averse to a view that, leaving somewhat aside the awkward question of "God as a person", would identify Man-Independent Reality with the notion we have of some divine Being.And at the end of his statement on receiving the Templeton Prize:
I consider I have sound reasons to believe in the ground of things I mentioned,lying beyond our ability at conceptualizing and which from time immemorial thinkers, less naive than was often thought, called “the Divine.”
It also raises a second question, a question about the exact nature of the "veiled" Reality of which d'Espagnat speaks and writes. Is it the same idea of Being that we find in traditional metaphysical study, or is it something different?