Meanehile, the french word for "map" is "carte."
Is there any relationship? Or coincidence?
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As you say, “Cartesian” is from the Latinised form of the family name “Descartes”. This derives from the one-time place name “Les Cartes”. So “Descartes” means “from (the place called) Les Cartes”. However, I have not found any satisfactory explanation for this toponym. It could be from the plural of carte, “playing card, map”, but this does not sound like a very plausible name for a village.
Otherwise, do you know if Descartes himself (writing of course in Latin) ever referred to the co-ordinate system as a “charta”? Maybe you would get a better answer in the “History of science and mathematics" forum.