Similar to my other question about her colonies I am interested in knowing what happened to the french royal navy of the period. Some ships must have been at sea and only learned the news as they returned to port and their unfortunate captains and officers, possibly, executed or jailed? Furthermore, what of the fleets in port, did the sailors mutineer or hold steadfast? Were some ships sabotaged, sunk or torched to stop them landing in revolutionary hands? The question is mostly centered on the early 1790s.
The French navy suffered considerably due to the French revolution. Having finished the American War of Independence on something approaching a high (comparatively speaking), the French navy suffered a reverse that it never fully recovered from until well after the finish of the Napoleonic Wars.
Like most other European navies of the time, the officers were often from the upper-classes and, as you probably guessed, there was a large-scale purge of these officers in the early period in question. Their replacements were rarely of high quality and, too often, had little or no experience of commanding a warship at sea, much less a warship in combat. Many of the aristocratic officer class fled the country (or failed to return) and these emigrés wound up in the navies of Britain, Austria and Russia fighting against their former homeland.
Also the fervour of revolution and its ideal of equality meant that these replacement officers often had little control over the ship's crews. As an example, at the start of 1793 Vice-Admiral Morard de Galles took a small squadron to sea from Brest, upon their return he commented on the crew:
The vaunted ardour which is attributed to them, consists uniquely of the words of "patriot" and "patriotism" which they repeat ceaselessly, and the acclamations of "Vive la Nation", "Vive la République" when they are flattered. Nothing can make them attend their duties.
Another consequence of the revolution was the disbanding of the Marine Artillery Corps (over 5,000 men), whose skilled crew men were considered too elitist. This left the navy with untrained men servicing the guns and the result was to limit the navy's fighting ability considerably.
In addition, the dockyards were not immune to the revolution and were centres of uprisings as much as the big cities. After the revolution, like the new ship's officers, the dockyard managers and commandants found that the workforce wasn't as keen on taking orders as it had been. This lead to a loss in efficiency in building and repairing vessels (and an increase in other losses), with the natural result that fewer ships in the navy were fully fit to go to sea.
While the French army was saved from destruction during the revolution by men such as Carnot and the emergence of Napoleon, there was no equivalent saviour for the French navy.
To add to the self-made destruction, the royalist french forces occupying Toulon invited in the British and Spanish to assist them (August 1793). The British helped themselves to a number of ships in the port, including the 120-gun Commerce de Marseilles (one of the largest warships of the period), the Spanish took a couple and the Neapolitans had a trio of sloops. When Napoleon finally overran Toulon, the evacuating forces sank and/or burned a significant number of the remaining ships, including 9 ships-of-the-line. This left the French Mediterranean fleet in something of a state (although, thanks to events elsewhere this didn't prove too much of a problem until after the Battle of the Nile in 1798)
While the Atlantic ports didn't suffer in the same way as Toulon, they did have their own problems as can be seen with the situation at Brest. At Brest, Rear-Admiral Villaret-Joyeuse (who, despite his noble birth, was trusted by the post-revolutionary governments) had taken a firm hand when he replaced Admiral de Galles and brought both the port and fleet under some control. He was able to get a number of squadrons to sea to cover incoming grain shipments from America. Despite losing 7 ships of the line during the "Glorious First of June" battle with the British Fleet, his successes in saving these merchant shipments, let him keep his head and control of the fleet.
However, the poverty of the Brest shipyard at the time is illustrated by a sortie by the fleet intended to cover three squadron operations in the Mediterranean, Indian Ocean and West Indies at the end of 1794. Many of the ships left port without fitting out properly and most left with just two weeks worth of provisions on board (by comparision, British ships of the time typically went to sea with 3-6 months of provisions). This lack of equipment is said to have contributed to the loss of five ships from the fleet in a storm.
refs: "Navies of the Napoleonic Era", D. Smith (Schiffer Military History, 2004) "A History of the French Navy", E.H.Jenkins (Macdonald and Janes, 1973) "Fleet Battle and Blockade", ed. R.Gardiner (Chatham Publishing, 1996)