Why did the French support the Americans?

Because Britain was the traditional enemy of France.

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A driver of political discourse in France in 1760 was the national humiliation experienced during the Seven Years War (1756-1763). A demoralizing, utter defeat in 1763 had confirmed the age-old principal enemy status upon the English. The conquest was all the more demoralizing because of the incredible advancements since enjoyed by the wealthy victors. Great Britain as she was now called, dominated the waves for certain, but, from the wounded French perspective, they seemed to rule everywhere else too.

This resentment fed France's "fund-at-all-costs" support for the Americans' fight with their colonial masters during the American Revolution (1775-1783). Vast resources were directed to funding the anti-British side. This was occurring at a time of worsening financial conditions and ineffectual management of the situation by the royal governments of Louis XV and XVI. A lack of critical debate about royal policy in the political court order and poor representation of the commercial class had combined with a prolific up swell in philosophical theory, dominated by Voltaire and Rousseau. France also suffered from a collapsing infrastructure and comparatively inefficient farming industry and trade sectors. Britain on the other hand, was heavily involved in investment, in roads, boats and boatyards, an Excellent canal system and a burgeoning new railway system and was commercially benefiting from its natural island location. It's small size and defined borders assisted the emergence of a new breed of Englishman, who spread by courtesy of the best naval force ever seen, to large and productive new colonies.

By the Treaty of Paris in February 1763, Britain had taken ownership of a handful of lucrative colonies in Central America and the Caribbean islands, of Madras in India, and almost the entire north American continent. Basically, the French hated the English and wanted to humiliate them.