I'm not sure what you are asking about exactly but there is the Angle-French War of 1778-1783, which can be viewed as an extension of covert assistance given by France, Netherlands, and Spain to the Americans, into an overt war against Britain.

Perhaps you can better explain what it is you are asking.

An important concept in Europe in the 17th and 18th centuries was the 'balance of power'. Major powers, chiefly the ones you mentioned in your question, wanted to prevent any other power from achieving a dominating position on in Europe. The balance of power is a system where states would form alliances against whichever other state threatened domination. The goal was not to preserve peace, but to preserve the sovereignty and independence of each European state.

In the 17th century many wars with varying coalitions were fought within Europe, but during the 18th century the attention shifted to the colonies. The War of the Spanish Succession (1702-1713) was fought by a grand alliance consisting of England, the Dutch Republic, the Austrian emperor, Brandenburg, Portugal, and Savoy. They fought to prevent the Bourbon family - who were the royal family of France and were to also become the royal family of Spain - from getting too much power. In the end France/Spain lost; a Bourbon was allowed on the Spanish throne, but the Spanish possessions in Europe were partitioned. Britain emerged as the new greatest power.

The War of the Austrian Succession (1740-1748) was the first in which overseas successes/losses played a major role. France and allies were powerful on the European continent, but the capture by British and allied forces of the French fortress of Louisburg in America and the subsequent blockade of the French West Indies forced the French to negotiate a peace. In the interest of the balance of power, Britain and France agreed to return to the situation before the war, i.e. all occupied territories and fortresses were returned to their respective owners.

The Seven Year's War (1756-1763) once again saw Britain and France going head to head, this with swapped alliances (because of balance of power each country which alliance served their interests best). Some of the fighting took place in Europe, but by now the center of gravity had shifted to the colonies. Both Britain and France were by now dependent on trade with their colonies, and the colonies provided a lot more easy pickings than the heavily defended European countries. So the most important fights of this war took place in India and America. In the end France lost the war and was forced to abandon North America.

This set the stage for the American Revolution, at least as far as European involvement is concerned. For two centuries European states had fought each other both in Europe and abroad. The fights in Europe had proven to be costly and difficult, whereas the fights in the colonies had proven to be very effective. Since dependence on trade with the colonies had grown over the years, a victory in the colonies would force a state on its knees. This is the answer to your question why there were no major military campaigns in Europe. The campaigns in Europe had been fought over and over again and were quite predictable (Britain dominates the seas while standing no chance in a continental fight, France dominates the continent, with other states playing roles of varying importance either in their own right or as allies). These states knew that the colonies were the place were the war(s) would be decided. So during the American War of Independence you've got the Anglo-French War and the Fourth (!) Anglo-Dutch War both being fought primarily on the seas and overseas.

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Source: I used Palmer's History of the Modern World for making sure I got my facts straight in this answer.