Final answer:
John Adams' major accomplishment was the establishment of the U.S. Navy, enhancing America's defense capabilities and successes in the Caribbean during the Quasi-War with France.
Step-by-step explanation:
One major accomplishment of John Adams' presidency was the creation and development of the U.S. Navy. During his term, Adams dealt with the Quasi-War with France, and the establishment of the Navy significantly strengthened national defense, allowing American ships to have success in conflicts in the Caribbean against French forces. This embodiment of a strong maritime force ultimately gave the United States an advantage in the region and contributed significantly to the nation's emerging strength on the international stage.