Did I mention that at the time, Jone's ship was sinking? And just to top it off, he won that battle and took the Serapis as his own. After the war, he decided to stay in Europe, first living in Paris, then moving to Russia and taking a job in their navy. He eventually left after political backstabbing a smear campaign directed against him by jealous Russian officers and returned to Paris, where he died on July 18, 1792. He was buried at St. Louis Cemetary, which belonged to the Royal Family of France. Unfortunately, the French Revolution hit not long after, the Revolutionary government that took over sold the land and I guess in the chaos, the everybody forgot "oh hey, there are bodies buried here, somebody might want to note that."
Something worth noting, however, is that when Jones died, a wealthy French admirer of his donated money to have his body preserved in alcohol and buried in a lead coffin, so that way the Americans could better identify him if they decided to reclaim his body at a later point. There was one attempt in 1845 by a Colonel named John Sherburne and this attempt was supported by at least the Navy, but ultimately fell through in 1851 when some of Jones' relatives from Scotland objected to his disinterment. Of course, the main obstacle in reclaiming his body wasn't his relatives, but the fact that nobody knew where he was buried.
Initially, his coffin was placed in Bancroft Hall of the Academy, after a big ceremony that included a eulogy by Roosevelt. In 1913, his body was moved to the crypt of the Naval Academy's Chapel and re-interred in a big marble and bronze sarcophagus and as a lasting tribute to his importance as Father of the Navy, an honor guard of Marines stand guard when the crypt open to the public, which is every day.