France and Spanish warships were patrolling off the coast of North America and preventing the English from bringing in reinforcements. Various naval battles happened.

But ever more important was the invasion of British Isles that the French and Spanish were preparing. That literally locked down the British army and navy to Britain and made it impossible for them to supply the colonial armies.

So when the French volunteers, Prussian trainers arrived in North America on top of that, the tide of war has changed.

It wasn't just the Americans, the French also supported the indian rebels against the British. It was the French connection that made popular the tales of indian resistance in America, and how Hyder Ali and Tipu Sultan (father and son, rulers of then Mysore state in colonial India) became inspirational heroes for the American revolutionaries. (Why American revolutionaries admired the rebels of Mysore - https://aeon.co/essays/why-american-revolutionaries-admired-... ). Indeed, some speculate that if the French had not weakened, the Mysore rulers might have been successful in chasing away the British from large parts of India too.

But ofcourse, as soon as America got its independence, it chose to follow the British and become an imperialist too. The defeat in America also made the British obsessed about holding on to India, and change their strategy - a few decades later, they took over the direct administration of India.