That is lovely. I also think it looks more like a "G" than a "C". Antique and vintage linen sheets are divine, and I could not live without mine in the hot summer months. It sure looks like linen in the photos, but that is not conclusive. If you think it has the feel of linen, that cool touch and crisp hand that seems to never really completely wash out (thank goodness), then it probably IS linen. It will be hard to tell if these are metis. A burn test will be inconclusive unless you have the nose of a trained expert and even then they really both smell the same. Without chemical or microscopic testing available to you, I might recommend the water spot test. But since metis has both cotton and linen fibers in varying amounts, that test might not work very well either.
My best test is experience in handling them over the years, so "if it feels like linen, it probably is".
A basic water spot test is: Take the fabric and smooth it out a bit taught, place it raised up from any surface so air can go underneath. You might try placing it between two short piles of books, etc. Take an eye dropper and from an inch or two above the textile, drop 1 good sized drop of water. Watch CAREFULLY as this clue will happen very fast. If the textile is pure linen, the water spot will barely (or not at all) spread out into the fibers from where it initially fell. If it is cotton, the water spot will spread out and change shape, getting larger and blurry shaped as it is absorbed into the cotton fibers.
This is not foolproof, but it is helpful in many cases.
It is really a wonderful sheet.