Again, it doesn't really have to fight a full-scale war. The French Navy could have dealt with the Union Navy without too much trouble. There would be no need to contribute troops. With French recognition comes loans from French banks. IOTL, a major loan to the Confederacy came from the Erlanger bank even WITHOUT French recognition; with such recognition, we might see loans from much bigger banks such as the French branch of the Rothschilds. More importantly, diplomatic recognition of the Confederacy gives it credibility that will both allow it to float loans on the bond markets of Paris, London, Amsterdam and Frankfurt much more successfully than IOTL and will give the Peace Democrats within the United States a much more credible political position.
I think you are overestimating the willingness of European bankers to invest in something so high risk as the Confederate economy. Even if the South had won, it was extremely unlikely that said bankers would ever have seen one cent of those loans paid back. IOTL they had to eat every loan made as it was. French intervention would mean that trade (and any loans made to the US) would be lost too.
The Rothschilds would know this better by far than us.
A useful ally in the quest to gain control of Mexico and a leg up on a valuable source of raw materials in the effort to economically catch up to Great Britain.
I think you are underestimating the costs of two transatlantic wars (even if one is naval, and do they have the facilities to wage even an "easy" campaign?).
Neither Mexico in 1861-67 or Prussia in 1870-71 was trying to blockade the Confederacy.
I think you are underestimating Bismarck's skills in exploiting French weaknesses on the Continent.
If there's actual military support, or even strong financial support, that might butterfly away the Great Germany. Without the French threat to Metz (either because they're busy elsewhere, or because they're clearly weak due to pouring money down a hole, or because they've just been given good evidence that their army at this point isn't as good as they think it is against a modern power), then the South German Federation doesn't align with Prussia; rather, it looks to Austria. Hence, Germany is smaller - if it forms at all.
And maybe with less of a threat the South German Federation is more likely to go with the Prussians, who offer the indulgence of German Nationalism better than the weaker Austrians, who have the problems of ethnic distractions in Hungary and in much of the rest of the Balkans. Germany for the Germans.
And based on Austria's anemic performance in the Austro-Prussian War, its likely the Prussians get their own way anyways.
Obviously not. The French could break the blockade with their own navy without too much trouble, though.
Except in terms of logistics.
If the French recognize the Confederacy but do not actively intervene, it still helps the Confederacy enormously simply by raising its credit rating. A bank like Barings or Rothschilds will be much more likely to invest in the bonds of a recognized nation than an unrecognized rebel government. And it also will strengthen the hand of the Peace Democrats as 1864 approaches.
More likely investing into the sinkhole that is the CSA makes France even weaker economically when faced by a resurgent Prussia. And I really think you are overestimating Nappy III's strategic insight.
But recognition without intervention is unlikely in any event, because Lincoln and Seward had made it clear to both the British and the French that recognition of the Confederacy was a casus belli.
And why the British were determined NOT to recognize the CSA short of a Saratoga-level victory by the South.
In the ARW, the American Rebels destroyed two major armies (Saratoga & Yorktown), and four minor ones (Trenton, Bennington, Kings Mountain, Cowpens). Five minor ones, if you want to count the shredding the British took at Guilford Court House (a British victory but a major embarrassment). The American Rebels in the ARW were not SUPPOSED to win standup fights with the British Army, certainly not to the point where the British force would be completely destroyed (or captured, if a siege). So when they did, it caught major attention from not only France, but Spain, Holland, and eventually even Russia (in their league of neutrality).
No such battles ever occurred in the American Civil War. (1) The closest I suppose would be the First Battle of Bull Run. But even there, the Confederates utterly lacked the ability to exploit their advantage. Also, the level of forces between the USA and CSA was never so imbalanced as it was between the British Empire and the Thirteen Colonies. So Lincoln had a lot more room to play with in the 'expectations game' than Lord North ever did.
1) Indeed, though not realized at the time, (2) the level of defensive firepower in the ACW versus the ARW was such that save for sieges (Fort Donelson, Vicksburg) only one army on either side was ever truly destroyed in the field of battle (Nashville). (3)
2) That this was NOT known was another of those things that the North had in its pocket without ever knowing it. So they could always play down Confederate victories to the level of "at least we survived" post-battle spin.
3) There are those that claim that the pitiful remnants that clung together post-Nashville under their new commander Nathan Bedford Forrest still constituted a real army. I do not agree.