(CF) A subject, S, is epistemically justified in believing a belief p if and only if either p is indubitable or p is entailed by beliefs that are such that S is epistemically justified in believing them.
It is easy as pie to show that Descartes himself is not a 'Cartesian Foundationalist' in this sense -- indeed, I think it is fairly clear that none of the major Cartesians are. (However much they may be in other senses.) It's not a Cartesian position, suggestive thought it may be of Descartes's method of doubt. For one thing, putting Descartes's epistemology in terms of justification of beliefs distorts his real interest -- the elimination of error in our beliefs and opinions -- in a number of different ways. But more seriously than this, in Descartes's epistemology you can believe things that are neither indubitable nor implied by things that are indubitable. One such category of beliefs consists of those relating to the external world. Descartes does not completely salvage the external world from the method of doubt. He manages to find a general reliability principle -- 'God is not a deceiver' -- but this does not give us certainty in any of our beliefs about bodies, except the beliefs that bodies exist and that they are subject to the principles of geometry.* There is plenty that does not fall under these but about which we can reasonably free ourselves from doubt. As Descartes says in Meditation VI:
As far as the remaining matters are concerned, which are either merely particular (for example, that the sun is of such and such a size or shape, and so on) or less clearly understood (for example, light, sound, pain, and the like), evne though these matters are very doubtful and uncertain, nevertheless the fact that God is no deceiver (and thus no falsity can be found in my opinions, unless there is also in me a faculty given by God for the purpose of rectifying this falsity) offers me a definite hope of reaching the truth even in these matters.
Thus, Descartes says, we shouldn't doubt that we each have bodies that need to be fed, to which we are intimately joined, that operate in an environment of other bodies that have differences in some way corresponding to my sensations, and so forth. On Descartes's view, none of these are indubitable; none are entailed by indubitable beliefs; they are fallible beliefs. But they are legitimate beliefs that we should not doubt (as long as we recognize our inability to prove them rigorously). Thus Descartes holds that there are beliefs that meet neither of the criteria in the above definition of 'Cartesian Foundationalism'.
* It should be said that the exact scope of what falls under certainty with regard to the external world is a matter of some contention in Descartes scholarship; Descartes himself is not very precise about where the limits of such certainty fall.
