Probably no independence. Fear of the French would have stopped many from supporting separation from Britain. Additionally, you would have seen a limit in migration across the Appalachians and an economic crisis in Virginia and Pennsylvania as land speculators saw their holdings crash in value. Interesting to think that George Washington might have gone bankrupt or close to it, as he was very heavily leveraged in land speculation. As far as the map, little would have changed in North America, but the Caribbean would have seen a lot of change and transition. It's hard to say what impact that would have had on the colonies, but it would have driven the price of some imports up and driven down the value of some exports.