Peel carrots and cut into 1/4-inch thick slivers, on an extreme bias, cutting the carrots into long decorative spears a couple inches long. Save the ends of the carrot for another use.
Snip green beans and cut into lengths about the same as the carrots. If you have the patience, split (French Cut) each green bean as well. It takes a few minutes, but it is so nice!
Cook the green beans in salted boiling water until 1/2 done, add carrots and cook until just tender (test often – take care not to overcook). Drain, rinse and serve decoratively – arranged around meats as an edible garnish. Dress with a pat of butter and a sprinkle of fleur de sel.
Or shock in ice water and warm gently when time to serve, finishing with butter and fleur de sel.