Statesmen typically forgo revenge, seeing it as a costly indulgence with incalculable risks. What happens, though, when passion or some more elaborate calculation prompts them to settle old scores? The role that France and Spain played in the American Revolution offers a revealing test case. As Larrie Ferreiro notes in “Brothers at Arms,” the assistance of these two countries kept the cause of rebellion alive in the colonies during a critical early stage, and direct French intervention in 1778 transformed a civil war in the British Empire into a global conflict. The motives behind these interventions, he shows, had less to do with freeing the colonies from an oppressive ruler than with skewering a longstanding adversary.

Americans understandably miss the larger story that Mr. Ferreiro, an instructor at George Mason University and the Stevens Institute of Technology, recounts in his wide-ranging study. He draws attention to people and events that George Washington and the other eminent founders routinely overshadow. The result is a familiar story told from a new vantage point. Revisionist in the best sense, Mr. Ferreiro’s book deftly locates the war within the rivalrous 18th-century Atlantic world.

The story begins with Britain’s sweeping victory in the Seven Years’ War (1754-1763), which left France and Spain—ruled by branches of the same Bourbon dynasty—with feelings of bitter resentment toward the power that had vanquished them. Britain’s capture of Havana in 1762 underlined to the Spanish the vulnerability of their American empire. France’s foreign minister, the Duke of Choiseul, argued in the 1760s that weakening the Royal Navy’s supremacy would reduce the danger that both countries faced from Britain while restoring Europe’s balance of power. Growing unrest in America offered an opening to pursue that aim.

The fortunes of war added a new impetus: France’s expulsion from Canada ended a threat to English-speaking colonists that had kept them dependent on Britain for protection, and Britain’s efforts, soon after, to tighten control and enforce taxation sparked colonial resistance. Ironically, during the 1765 Stamp Act crisis, French agents reported that Virginians spoke of France coming to their rescue if fighting broke out. The news confirmed Choiseul’s strategy even if he and his colleagues saw revolution in America more as a distant prospect than a looming inevitability.

When Britain prohibited the shipment of arms and gunpowder to America in late 1774, foreign help came first from private merchants: Spanish and French traders linked rebellious colonists with European manufacturers, particularly the Dutch and Belgian gun makers of Zaandam and Liège. Governments on the continent acted cautiously, permitting and then facilitating such efforts. Weapons sent up the Mississippi from Spanish-ruled New Orleans replenished vital stores. Pierre Beaumarchais, better known for writing “The Marriage of Figaro,” negotiated a deal to trade French gunpowder for American tobacco. Without French aid, he warned in February 1776, Americans would face quick defeat and France’s Caribbean colonies would be more susceptible to British attack. Count Vergennes, who had become France’s foreign minister in 1774, persuaded his Spanish counterpart to join in an effort to finance America purchases. The aid, they agreed, “must always be cloaked and hidden and only appear to be commercial in nature, so that we may at any time deny it.”