Thanks for your answers but you are focusing too much on the French side of thing (which is entirely my fault).
Forget for now about the French thing and focus more on the fleet I "designed" and on the more generic questions on fleet building I have (as you all know space is not my cup of tea).
I thought I had at least indirectly answered some of it, but I'll go for a more direct response.
Ship types:
Ship classifications in BattleTech/BattleSpace/AeroTech are practically meaningless. What, after all, is the difference between a battleship and a battlecruiser? In canon designs, both tend to have eggshell-thin armor, both are able to destroy the other in as little as a single broadside (something which has happened about once in real naval warfare, Bismarck vs Hood/Prince of Wales).
Looking at the McKenna and the Black Lion in 3057 Revised, the McKenna may have 50% more armor, but the Black Lion is so over-armed that it makes the difference meaningless. Either can destroy the other in a single turn, and it can easily turn into mutual-destruction, as well.
In the real-world, what few official designations existed for warship classes were based on firepower. The Washington and London Naval Treaties established that "Heavy Cruisers" (a type it created) carried guns heavier than 6 inches (150mm), while "light cruisers" (another type it created) carried guns over 5 inches up to 6 inches. Tonnage limits were set on heavy cruisers, but not specifically on light cruisers, which resulted in things like USS St Louis and USS Helena, technically light cruisers due to their 6 inch armament, but displacing the same 10,000 tons as the "treaty cruiser" types of heavy cruiser which preceeded them, armed with 8 inch guns. These heavy cruisers had an advantage of longer-range firepower, but the 6 inch gun fired faster. Below about 10,000 yards (knife-fighting range for WWII warships) the light cruisers were actually more destructive, because their lighter guns fired nearly three times as fast, letting them get more destruction on enemy targets.
BattleTech ignores the fact that, in general, heavier guns are able to shoot further than lighter guns, and anything resembling a rate-of-fire advantage. It also ignores the fact that a single turret on a WWII battleship tended to weigh more than an entire destroyer, which rarely came in at more than 2000 tons. Battleships also tended weigh ~20 times as much as destroyers. USS Colorado, of 32,000 tons, was designed when "modern" destroyers displaced 1,000 tons. USS Iowa, of 45,000 tons, was designed around the same time as the 2000-ton Fletcher-class destroyers. By the same ratios, the minimum 100,000-ton "warship" is the right size to play destroyer to the likes of the McKenna and Texas, rather than the 500,000 to 600,000 ton monstrosities.
Going back to our Black Lion/McKenna comparison, however, what does the Black Lion have that makes it a "battlecruiser"? It's no faster, and when the battlecruiser role was invented about 1906, the requirement was for a ship that had battleship-type weapons with less armor and more speed. Black Lion is short on armor (but not enough so to make it important) but lacks the extra speed. So it's much more a "light battleship" than a "battlecruiser" by any definition which cares about speed. But by the time of the Queen Elizabeth class (1913), ships could have the high speed and full battleship-level protection, creating the "fast battleship" and essentially rendering the Battlecruiser obsolete. Though always designated a battlecruiser in official literature, HMS Hood was frequently considered a "fast battleship" by people outside the Royal Navy, considered to have equal protection and firepower of the Queen Elizabeths, but with greater speed.
In WWII, destroyers were fast, completely unarmored, and armed with 4 to 5 inch guns and torpedoes. Many light and some heavy cruisers had equal speed, though all heavy cruisers had some protection. There are no documented instances of a destroyer sinking a vessel larger than a heavy cruiser, however. Nor are there instances of any cruisers sinking a battleship, largely because of the ineffectiveness of the weapons on these ships at penetrating the armor of heavier warships (the heavy cruisers sunk by destroyers were always sunk via torpedoes, for which BT has no analogue other than nuclear-armed capital missiles, and even that's a poor one).
The doctrinal reason ships other than battleships existed in the era of classic large-scale navies was to protect the heavier warships from torpedoes (whether carried by aircraft, other light ships, or submarines). Destroyers were originally named "torpedo boat destroyers" and came about to protect slow, ungainly battleships from light, nimble, short-range torpedo-carrying ships. They were later adapted for anti-submarine and anti-aircraft work, though eventually both the US and British navies designed light cruisers for the sole purpose of air defense, which were excellent at their designed task and generally utter failures against other warships. BT's ridiculous rules on fire-control and the number of weapons per firing arc make this very difficult to emulate, though easier with the introduction of sub-capital weapons.
Realistically, the "destroyer" role of a small, fast escort should probably be played by DropShips. They'll still have the fire control/weapon arc issue, but they can have better speed curves to distinguish themselves from other types of warships.
Cruisers should probably be smaller, less expensive battleships, though BT makes it quite easy for these types of cruisers to destroy a battleship, especially with superior numbers. I'd personally go for quantity over quality under BattleTech's rules, because bigger size gains you practically nothing.
In the world of infrastructure, if you're using these ships for an average of 200 years apiece (only a little shorter than most SLDF designs were used by the SLDF), then you could realistically build them all with a single construction slip, assuming it was always building a new warship. Realistically, you'd probably want more like 10. In real navies, warships can expect to spend 10-30% of their active lives undergoing maintenance, upgrades, and repairs in a shipyard. So 10 to 20 would give you sufficient space to handle routine maintenance (but not necessarily battle damage) as well as construction.
How you produce and maintain a navy is less concrete. The main thing, historically, needed to "produce" a Navy is political will. Industry helps, but Brazil, Argentina, and Chile once owned & operated battleships. Today, with the recent launch of China's first aircraft carrier they have exactly the same number as Thailand, and, depending on how one defines "aircraft carrier," two fewer than Japan's "Maritime Self Defense Force". GDP is a poor measure of a country's ability to support a military, as Luxemburg routinely scores in the top 5 of GDP measurements, while the United States rarely breaks into the top 10. It's all about political willpower. While the South American naval arms race was going on in the early 20th century none of the countries involved were "industrialized;" they just had the desire to be seen as "battleship nations" and so ordered battleships (from Great Britain, generally). Much the way countries today desire to be seen as "nuclear" nations and so waste a great deal of money developing nuclear bombs, or "space nations" and throw a lot of money at sending things into orbit. It's a matter of national pride more than industrial capacity, if the nation is willing to order the warships elsewhere.
