As with OTL, France became the hegemon of Central Europe, dominating their Northern German vassals, with their AH allies dominating the south. Prussia, while still formidable, fell into civil chaos, rising from the ashes as the communist Prussia we all know and love, later forming the Triple Alliance alongside Britain and Russia against France, AH, and Italy in 1914.
A Prussian victory could mean anything, but a peaceful union into some united German nation, I highly doubt it. Most of the German states, particularly Bavaria, would never surrender their autonomy to Prussian dominance. Likewise, Berlin would never accept an HRE-esque set up. German unification would no doubt come into being through war.
The state of France would matter a ton here. How badly were they defeated? Napoleon III, at the time, was very unpopular. A French defeat sprinkled with an army is disarray could easily see the monarchy overthrown, and a communist coup taking control. If Prussia gives France time to recover, then I could see the French and Austrians joining the southern German states against Prussia and Britain.
Well supposedly Napoleon III was going to visit the troops near the border one day, but was held up by a bad stomach flu, and a Coloniel once told Napoleon V that when he was a soldier, his superior had drawn up plans to replace his grandfather as necessary. Dunno how true it was, but Napoleon V certainly found it unamusing
I don't believe Napoléon III's régime was ever in doubt. In fact he won the 1870 referendum in a landslide before the war. The victory was simply the cherry on the cake.
It did however make permanent the idea that the Emperor should play an active role in the military (although Napoléon III was much less involved in the battle plan against Prussia than the propaganda claimed). Ultimately this led to Napoléon V's controversial intervention in Mozambique.
I don't think we can assume a French defeat would be the mirror image of the actual Prussian defeat. It would be a blow to the reputation of the Emperor, certainly. But the régime was already evolving to become more constitutional and it was known that he was going to abdicate upon the Prince Imperial's 18th birthday. Plus his reconstruction of Paris made it more difficult for groups to barricade the streets.
Now that you mention it, African colonization would be far different.
Spain took Europe's diplomatic shock to start carving their way back to some degree of prominence, subsuming Morocco, conquering Libya and parts of Arabia from the ottomans, even claiming parts of the Kongo and korea. It didn't save them from the spanish civil war in the 30s, or their defeat in WW1, but it did prevent a total Spain screw.
France, like you said, annexed Mozambique after Portugal lost control of it due to a socialist-democratic revolution. Plus the stuff in Algiers. They also yoinked the lion's share (rooster share?) Of the Kongo. it was home to some of the worst colonial exploitation of anyone for a long time, but after Napoleon V's Star Map to properly connect it to Mozambique, it shed that and began to become a vital industrial base with strong social equality, as the French Empire adopted a more civic nationalism than the other empires.
Honestly I feel bad for Britain- the Cape, Eypt and even Nigeria weren't bad, but with the French having one contiguous realm, they were shunted from the best of Africa.
King Leopold II of Belgium once mentioned that Belgium was too threatened by the chaos in Central Europe and the ascendant France to pursue the project, but he wanted a chunk of the kongo. While I doubt it could happen (look at belgium, please), he was a charitable man on continent, and Belgium was indeed a civic nationality, so I imagine he'd be better than pre-Star Map France.
But if Prussia wins the war, they're suddenly in a position to change
Everything -did they really want that many colonies though?