I believe French chic is something that has to be learned at an early age.
The women I have met who had it, or the Spanish or Italian counterpart of it, had been brought up from the age of 10 to make the best of their appearance, which at that age was concerned only with correct deportment, good manners and learning to choose clothes and combine them correctly.
Later, at about 14, they were taught to converse politely in adult company and never, never to go anywhere, in some families not even to leave their own rooms, without making quite sure that clothes and shoes matched and that their hair and nails were presentable.
Mothers, aunts, and more especially grandmothers were quite merciless in their remarks if one slipped up. Girls were expected to look in a mirror and assess their good and bad points, then discuss how to make the good points more noticeable and how to conceal the unfortunate ones.
To a lesser extent, until the 1970s, Scandinavian, Austrian, Swiss and German girls learned these things too, whereas in Britian where I lived for most of the year the attitude was that as long as you and your clothes were clean that was all that mattered, and teenage girls were more or less expected to be shy, tongue-tied and as my scandalised Danish grandmother put it, "Behave like boys and look as if they had dressed by guesswork."
In the British girl's defence, obviously spending 40 something weeks of the year in school uniform hardly developed one's dress sense, nor could the clothes sold by the C&A, Lewis's or Marks and Sparks do anything at all towards making a gawky 15 year old feel confident about her appearance. (Clarkes' shoes did not help either.)
Cultural differences exist for better or worse and I do not believe that you can learn these things, however hard you want to and try to, as an adult if you have not been trained as a child.
Nowadays, only those women who still have their clothes tailored show any difference in the actual clothes, as all the rest of us are clothed by Hennes & Mauritz. Levi's and other international shops - but the woman inside the clothes has still been brought up to conform to one or other country's unexpressed expectations and therein lies the difference.