What would the modern population of an independent Corsica be? Being a nation with it's own centre and prestige, one would think there would be far less emigration and any infrastructure projects would be more well thought-out - not quite as great as the French Plan Terrier, but far more realistic and actually implemented.
I would think that a population around a million in the modern day is not out of the question. Corsica is a small country with a very mountainous interior, but if the port cities remain hubs of trade for one reason or another and Corti remains the official capitol, several settlements with six figure populations does not seem impossible.
It's also a very poor country, without a lot of clear paths towards generalized prosperity (although a relatively decent and even standard of living seems plausible). There will probably be less out-migration than IOTL, given that it will be an independent country, but especially in the face of social conflict and economic problems, people will be looking for a way off their little rock.
Which raises the question: where will they go? France is right there, but it's not a part of France, so that sort of migration may not be so seamless. One interesting place might be England, especially its port towns. One quick way off the island would be signing up with the Royal Navy, and if they have a base on the island (or just generally treat Corsican ports as friendly, especially given their assistance in freeing Corsica from Genoa), that might be the best option for a lot of young men looking for adventure, and after their service, they might end up in England (or its colonies) as merchant sailors or merchants or industrial workers. And once you have a starter population, established networks mean migration happens a lot more smoothly.
Peaky Blinders, but set in Bristol and with Corsicans, anyone?