This is a really complex problem, made even more complex by governments in exile and fleets sometime scuttling instead of surrendering even if ordered otherwise. There were military ships that were captured by all sides, just like there were ships that escaped to be part of Governments-in-exile but they weren't really significant in the scheme of things*, but the circumstances surrounding the various captures and 'escapes to serve with Governments-in-exile' are pretty complicated.
* The non-military fleet of Norway, on the other hand, was quite important to allied merchant marine capacity early on, while the allies also took good advantage of captured German merchant ships.
For example:
- Had Germany looked like it was going to seize the French fleet, there's a fair chance France would have scuttled, like they actually did in 1942 when the Germans tried. On the other hand, when the Allies took North Africa, significant naval forces, including a modern Battleship, changed sides without a fight, but that same battleship had taken part in fighting off an Allied attack earlier in the war.
- When Italy surrendered in 1943, the Italian navy sailed to Malta and surrendered to the Allies, but wasn't really used in an operational capacity due to concerns over reliability and loyalty, even though Italy had technically changed sides and they weren't captured but were still Italian ships fighting for Italy.
- Japan commandeered a number of captured vessels from the US, UK, Netherlands and China, even after it had sunk them first (it raised and repaired them, before using them).
- At the end of the war, remaining naval vessels were generally captured by the Allies, but most were scuttled or broken up.
At the end of the day, the only large transfers of vessels intact took place when one side already had overwhelming naval superiority. When the situation was more contested, there tended to be scuttlings or escapes to fight with Government's in exile, with limited captures that were fairly insignificant in the scheme of things. Given the complexity of the rules that would be required, for little benefit, and the risk of things going crazy haywire if done badly, at least starting off with it not being in the game makes a lot of sense, and maybe flesh it out later when there's more time available to focus on it.
That said - I think there's value in considering full (or mostly full) captures of fleets at the end of civil wars.
Well, some did, and only after a fight...
France is a special case, though, as there will be events to form the French State if the Third Republic falls.
look up Operation Catapult.
There were a number of French vessels that were operating in British or Commonwealth ports went straight to the Free French (obviously not those at Mers-el-Kabir!), others stayed with Vichy forces in colonial areas and generally went over to the Allies when the territories they were based in did, unless they were sunk first (Catapult), while others were stationed at Toulon, scuttled in 1942 and some of the smaller vessels were refloated and pressed into Italian or German service. It was such a mess, that at one point, one Bougainville-class sloop manned by Vichy (Bougainville) was sunk by a Free French Bouganville-classed sloop (Savorgnan de Brazza). Both French ships of the same class, both manned by French sailors, one sinking the other!
