Britain and France had been in an on-again-off-again series of wars for the better part of two centuries at the time, with the most recent example being what was called in Europe the Seven Years' War and in North America the French and Indian War. The government of France saw the revolution as a chance to weaken Britain in North America and divert British forces from Europe at little risk to France itself.
What the government of France did not see was that supporting democracy thousands of miles away might come back to bite them in the butt in a few years, when their own citizens noticed how well it was working out for the United States and decided they'd like some too. France supported the colonists because they opposed England.
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A number of countries used it as an opportunity to fight Great Britain.
According to the Declaration of Independence the King of England wanted to establish "absolute Tyranny over these" colonies.
African-Americans fought mostly for the patriots in the American Revolution.