You are asking for the etymology of the French family name "Descartes." I assume the Latin adjective was created after the philosopher. The des part is —sorry, I don't know the exact term but— "of the." Cartes is the plural of carte. Etymologically speaking, the family name is, "of the charts."
Flaminius is right. Any article, genitive marker [in guise of preposition or not] (French de, German von, Danish af), or other elements which do not belong to the basic word itself have to be peeled off a name before you can proceed with the latinization process.
In this case, Descarteslogically (eh...) becomes Cartesius – or not quite. It is a bit strange that the Latin ending is added to the French plural marker. I imagine the reason was to increase the name by one syllable. A philosopher with a name encroaching on the adjective of the word denoting “paper”, charteus, would perhaps not sound good.