I understand that it was an attempt for the French to get revenge against the British after the Seven Years' War. However, it seems to me to be a very risky move on the part of Louis XVI to support a revolution that could inspire a revolution against himself.
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Revenge and opportunity. France rebuilt its army and absolutely wanted to punish Britain and even reclaim some lost territory from the Seven Years War. They also feared that Britain was going to make huge concessions to the Thirteen Colonies and after the peace, ally with them to drive French and Spanish interests out of the West Indies. (During the Treaty of Paris in 1763, France had agreed to surrender Canada to Britain in exchange for keeping Guadaloupe and its money-making sugar plantations.).
When the American Revolution began, France remained neutral in Europe's continental disputes during this period, in order to avoid being drawn into any European conflicts while waging war with Britain. After 1778, Britain began to shift focus to defending its profitable sugar islands, which were seen as economically more valuable than New England. With island colonies in the Caribbean too, Spain and the Netherlands joined France in an anti-British coalition and preparations were made for a possible invasion of Britain itself.
While France was successful in its naval blockade of British forces at Yorktown in 1781 and Britain sued for peace, France delayed the war's end until 1783 in hopes of seizing territory in the West Indies and India. France's main fleet lost to Britain in the pivotal Battle of the Saintes in 1782. This doomed a planned Franco-Spanish invasion of Jamaica.
France didn't gain much from the peace treaty in 1783, besides the colonies of Tobago and Senegal. Louis XVI failed to realize his goals of recapturing Canada or more territory in the West Indies and India. The war had cost France 1,066 million livres (with much of this borrowed in high-interest loans) and the king's government concealed its true cost from the people, only claiming that expenditures had exceeded revenues. This had to be paid for with new taxes and the economic strain placed on the people would help to spark the French Revolution a few years later.
This is, I think, an example of a common logical fallacy. It’s easy to see in retrospect that Louis XVI’s support of the American Revolution may have kicked off a chain of events whose ideological underpinnings ultimately resulted in a similar Enlightenment-inspired revolution in France. At the time, however, it seems unlikely that such a “black swan” as it were, could have been predictable.
Indeed, Louis’ support of the Patriots was more than merely “revenge” for the Seven Years War. Instead, the American Revolution can more accurately be described as one piece of a much broader, longer lasting international conflict between the French and British (a sort of “Long War,” to borrow the phraseology of Philip Bobbitt of Yale). Going as far back as the French Wars of Religion - when the British supported French Huegonots against the monarchy - there was a nearly constant balancing of powers between the French and British. And, moving into the 18th century, the War of Austrian Succession and the War of Spanish Succession were widespread international conflicts that largely focused upon attempts (often led by the Brits) to check and cabin French expansion. The War of Spanish Succession is perhaps the clearest example, where the threat of a Bourbon monarch taking the Spanish throne (and the implied asymmetry into geopolitical power) was too much for the international system to stomach.
The Seven Years War and American Revolution, therefore, were mere blips in a much larger conflict. Louis XVI’ decision to support the Americans was not ideological, it was an element of grand strategy. The fact that the ideology on the ground ultimately created a conflagration in France can hardly be seen as something that was on the radar, so to speak, at the time.