I'm not really sure how one can over play it. France turned the American War of Independence into a global conflict. This greatly increased the financial strain on the already deep-in-debt British, and directly drew British regiments and naval assets from America to the Caribbean. French loans and gifts paid American soldiers and merchants, while Continental soldiers dressed in French wool carried French muskets. General Rochambeau persuaded Washington out of a difficult attack on New York in 1781 and instead orchestrated a joint operation with a French fleet that became the Battle of Yorktown. During the allied siege of that British base, there were more Frenchmen present than Americans, and French troops played at least as large a role as Washington's forces did.

Put simply, the American cause would have collapsed years before they could score a decisive victory without massive financial and material support from the French, and French soldiers played a central role in the decisive campaign on 1781.