I don't know. A protestant country, right between two major catholic countries, who are known to be quite agressive. I doubt it can survive for long. It would be interesting to see it survive though. It would most certainly mean that France won't be the single most strongest nation in Europe in the 17th and 18th century.
Yeah, it wouldn't last, the pope would call down a campaign from all sides. It's badly located and doesn't have the geographic and economic advantages of the Netherlands.