I think that it would mean that the WW1 analogue would not involve as many players,
CSA survival probably means French victory in Mexico to put Maximilien Hapsburg on the throne.
That is likely to butterfly away the Franco-Prussian War - Napoleon is not embarrassed by Mexican failure and is still entangled there so is less involved in German affairs, so giving Bismarck less leverage over the other German states than OTL's fear of France, and also France is less able to afford another war (so Napoleon doesn't want one) and may be better able to fight one if a continuing Mexican insurgency reveals issues with French artillery and doctrine early (so Otto doesn't want one).
The thing is, a France with A-L, and with no 1871 defeat, is really one of the biggest players on the board, which means that this sort of POD is one that is really hard to generalise for and really easy to be creative with.
Without 1871 war and French defeat, Franco-Russian postures against Germany are less strong. France has more difficulties being cordiale with Britain as with Alsace-Lorraine it remains a much stronger industrial power and competitor.
1873 Dreikaiserbund still goes ahead, though Bismarck has less influence. He pushes A-H to engage with Mexico (Hapsburg) while Britain is closer to USA.
Russian and Austro-Hungarian interests in the Balkans will remain at odds, leading to a shrinkage to a Zwiekaiserbund of some sort.
With a successful American venture and no Prussian humiliation, French colonial ambitions in Indochina and Africa may be more urgent. Maybe Fashoda is rather more contested?
Assuming only North German integration, then Franco-Prussian Great Game over southern Germany is parallel to Anglo-Russian Tournament of Shadows in Central Asia, and everybody dances around Africa.
By the end of the century, Britain has shifted away from Confederate cotton (Egyptian, rather than bad PR from slavery). CSA economy probably shifts towards slave-based industrialization of textile production to compete against USA Hudson Valley output, but is hampered by general tariff approaches. A smaller Germany means a much smaller HSF, with a corresponding decrease in British paranoia.
Spanish disengagement results in German Philippines and British Hawai'i (and maybe Wake, Guam, Midway as coaling stations).
Russo-Japanese War still probably happens on schedule. Britain is not anxious to go to war with Russia even if Dogger Bank incident happens as OTL.
If there is an Austro-Russian War after a Serbian terrorist act, it likely pulls in Germany and some support (loans and supplies mostly) from Britain and the USA on the Austrian side. There is no guarantee that France, the CSA, Mexico, Italy, or the Ottomans get involved (though all are possible, depending on how the early-1900s things in North Africa and the Balkans have gone). It's a given that the Anglo-American side can catastrophically harm trade to Mexico and/or the CSA if they get involved, which is a big argument for not doing so.
The wild card is Napoleon IV. Napoleon III's health was poor in the run up to the Franco-Prussian War and his death in 1873 is not likely to be very much later even without that conflict, leaving his son to rule instead of dying in an Anglo-Zulu War. Never having ruled the French Empire OTL, and without a clear idea of whether he would indeed become Emperor, or with what powers, had there been no war in 1870, you can pretty much do what you like with him.
Lunatic jingoist bent on Mitteleuropäische Kavallerie-Kriegsführung and whose armies surge into Luxembourg and Belgium within days of the news of a shooting in Sarajevo?
Anglophile connoisseur of bitters and ales who lets war slide on by?
Opportunist who fortifies in Europe while racing Japan to seize the Pacific and and Britain the African colonies?
Let France explode with civil war between Republicans, Bonapartists, and anarchists if you will, or let it rival Victorian Britain for the splendour of its isolation while a drang nach osten engulfs half a continent.
They are all possible, and as likely as you wish them to be.