Details of the sea battle, in which British ships chased and captured the French vessels, appear in the helmsman's log. The document, taken from the French ship Mont Blanc, was discovered by researchers from the British National Archives among the vessel's muster roll, the lists of payments to the crew on board.
Alistair Hanson, a historian at the National Archive, said: "This discovery is of significance because it provides us with a rare French eyewitness account of the battle. It will also be valuable to French genealogists who will be able to track those seamen who died."
The incident occurred towards the end of the Battle of Trafalgar as the boats Mont Blanc, Scipion, Duguay-Trouin and Formidable formed part of a vanguard of a combined fleet commanded by Rear Admiral Dumanoir Le Pelley.
Because of a breakdown in communication and a lack of wind, the ships were out of range for most of the battle. By the time they came face to face with the English, the battle had been all but won. The French fled but they were soon captured and became the only enemy vessels to be brought back to the UK.
Bruno Papparlardo, a naval historian at the National Archives, said: "The log is one of the most exciting finds in recent times for naval historians and anyone interested in the Battle of Trafalgar.
"Together with the muster rolls for the ship and rolls for the Duguay-Trouin, the Scipion and the Formidable, this unique find will allow us to be able to make direct comparisons between the British and the French ships and give us a better insight into their battle plans."
Dated 21 October to 22 October, 1805, one entry in the log reads: "At 3pm, our topgallant mast was damaged, at 4pm we recommenced firing, at 4.30pm a vessel caught fire whose nationality we assumed was English.
"Two English vessels were alongside at the same time. We were fighting each other in disorder and the two vessels mentioned were de-masted. While boarding we saw 15 de-masted vessels, including one on fire.
"At 5pm, the battle ended; at 5.30pm the sunset saw Cape Trafalgar to the east by south 6 or 7 leagues distant; at 6 in the evening the vessel that was on fire exploded."
On retreat, the French ships headed towards the Bay of Biscay and on 2 November, the entry reads: "At 10pm, we changed course under the wind, all sail on the port quarter, the enemy pursuing us always very closely. Weather very overcast and rainy."
But eventually the French were forced to capitulate and were taken captive by Captain Richard Strachan. Dated 4 November, 1805, the log reads: "The enemy's fire was most violent to leeward of us.
"Our squadron lay to windward. At 2 o'clock the Scipion lost her main top mast. The fire was most rapidly kept up on both sides. All our rigging was cut to pieces - moderate weather and a calm sea alone kept our masts up."
William Spencer, military historian at the National Archives, said: "The files were found by an intern who was researching some High Court Admiralty papers for the organisation. These rolls had gone unnoticed for a number of years.
"When a ship was captured in battle, the British sailors would be expected to bring the ships and the prisoners back to shore.
"They would take the ships' documents and muster rolls to the High Court Admiralty as proof of their capture in exchange for head-payments that would be shared amongst the seamen.
"Once payments had been made, the papers would have been filed as court evidence rather than as war documents, which is how they had lain hidden among the catalogue of documents for so long."