As a general rule (with exceptions) in the nineteenth and early twentieth century, the US has a tendency to massively demobilize between wars and massively mobilize during them.
So, for example, post-1865 it has a large army of trained men (not necessarily well trained, not in things like shooting, but they've got the deployment and artillery handled) and a large navy, much of it modern ironclads.
So fighting the US a that time is hard.
But from then until the late 1880s, the US did very little in terms of modernization or capability retention. As such, the US of 1880's fleet was mostly the fleet it had in service or building in 1865, and the US of 1880's army was very much a Civil War beast. (100-200 yards fighting range, 3" 1860s guns and so on).
Which is why the likelihood of a French war succeeding in the 1860s is high in 1860-2, then drops until 1866 or so, and then begins to (slowly) rise again.
Incidentally, in the late 1860s, the French would be bringing the Chassepot to a battle. That's a good, medium-long range, breech loading rifle started in full production in 1866 - while the US is still trying to decide what kind of trapdoor rifle to produce. (They built a lot of experimental models, though... so the capability is there to rush-build lever action breech-loaders.)
If for whatever reason France and the US get into a war, I would wonder how long Britain or Germany/Prussia might try to nip off parts of France or French Colonies.
Britain's not in full scale grab-all-colonies mode unless provoked, in this time period.
Prussia would be unlikely to do so, remember it took a French attack on Metz to make the German Federation gel into what would become Germany. It'd be just Prussia versus France, and that's not a risk to take lightly.
Though that does remind me - tactics-wise, the French are very different if the Austro-Prussian war has happened.
Before that date, the French tactics were pretty much like the American ones but more so - shock action, at the tip of a bayonet (instead of a close range firefight).
After that, as the French saw what good shooting did to Austrian shock columns, they switched mode entirely to fire-base tactics. This is a good way for an attacking American force (without the schwarmm tactics of an extended skirmish line with good shooting, or the Krupp artillery to blast the French out of their trenches) to get killed in large numbers.