The thrust of d’Espagnat’s work was on experimental tests of Bell’s theorem. The theorem states that either quantum mechanics is a complete description of the world or that if there is some reality beneath quantum mechanics, it must be nonlocal – that is, things can influence one another instantaneously regardless of how much space stretches between them, violating Einstein’s insistence that nothing can travel faster than the speed of light.
But the speed of light as we know it is only the speed of light in physical three-dimensional space. 3D space can be thought of as embedded in multi-dimensional spaces that our minds can never comprehend, and with that there can be unknowable metrics that have small distance in nDim-space even if immensely large in 3D. Visualize a sheet of paper (2D-space) folded over on itself. Two points 11 inches apart in 2D can be zero inches apart in 3D. Proceed by induction.
Let's be precise. First: Bell's Theorem doesn't quite say this. What it says it that if there is a completely deterministic hidden variable theory underlying quantum mechanics (as, say, classical physics) it cannot be a local hidden variable theory. Second: Einstein does not insist that nothing can travel faster than the speed of light, what he insists on is quite a bit weaker logically speaking: the velocity of light is an invariant independent of the constant velocity of an observer measured in any reference frame.
This is weaker because it allows plenty of things to travel faster than the speed of light. For example, two scissor blades closing towards each other at near light-speed have an apex which can move faster than light. Hypothetical particles on the other side of the light cone, such as tachyons, could also exist which do not violate this edict. Objects in our universe beyond our horizon lie outside our light cone: for mathematical if not physical purposes they are separated by spacelike distances and are moving "faster than the speed of light."
Finally, the combination of the two of these together as you phrase them suggests that quantum mechanics somehow supersedes Special Relativity. This is not true. Dirac formulated his theory of the electron in a way consistent with relativity, and the Klein-Gordon equation is also Lorentz invariant (check your Bjorken and Drell.)
Quantum teleportation -- of which the EPR thought experiment and experimental arrangements suggested by Bell are very simple examples -- does not violate the Special Theory, because there is no way a physical observer can use these means to actually transmit information. If he could, he would be able to change the relativistic meaning of simultaneity, and thus arrive at two observer locations which measured different speeds for light. Quantum mechanics does not allow this; paradoxically, although EPR implies "spooky action at a distance," it does not imply a violation of the Special Theory.
"Flatlander talk?"
We continue to struggle to define all things in terms of the dimensional parameters of which we are 'aware,' but at some point it becomes wise to accept that there are dimensional parameters that we are simply not equipped to discern, and thus unable to employ in our descriptions and computations.
We may not even have a reasonable realization of what 'travel' is.