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Rayon is a cellulose fibre that can, and is currently being used to an extent, as an alternative to cotton, silk, and other such substances. It was discovered as an alternative to silk in the late nineteenth century, and was the first man-made fibre. It doesn't require a very difficult process to create rayon, but the main restricting factor restricting its potential growth is that it will initially be more expensive than cotton and other alternatives. There is one circumstance where that factor doesn't exist, and that is Napoleonic France.
In Napoleonic France, trade with Britain was highly restricted due to the war going on. This meant that France, and indeed the rest of Europe, was blocked from getting various tropical goods. IOTL, this meant that sugarcane was no longer an option. Although sugar beets were discovered to have sugar pre-war, it was only during Napoleon and the lack of sugar from sugarcane that it became a major way to produce sugar. Otherwise, it would have simply been uneconomical to produce it. So, assuming Napoleonic France discovers rayon, could it then mean that it becomes a major competitor to cotton?