Certainly that has potential as a POD for the happiest TL ever. No Mexican Adventure, no Spanish unstability in the late 19th century, no Franco-Prussian War...
Why no Franco-Prussian War?
I don't think that Max was going to be sitting on the Spanish throne, and here is why:
In the aftermath of the Six Weeks' War, Napoleon III realizes that he has mis-judged the situation. Prussia is now a huge threat. The North German Confederation is seen, in France, as the embreyonic German state that it was (I believe that this is OTL so far?). So France tries to get some kind of alliance with the Austrians, but the Austrians aren't really having any of it.
The French, after all, were enemies of the Austrians not so long ago, and the French actually took land away from Austria, whereas Prussia just kicked them out of Germany.
In fact kicking them out of Germany wasn't even so bad, because Franz Josef was such a short-sighted conservative that he was so [unwilling to use/unaware of] growing German nationalism that could be used to his advantage. Broadly speaking, the Germans were looking to be united. They offered German leadership to Prussia in '48, but the Prussian King was such a brain-dead Holy Alliance conservative that he wouldn't accept it. If a Hapsburg ruler had been willing to manipulate nationalism for his own gain (a man like, say the Archduke Maximilian comes to mind) then he could have turned the Hapsburg old control over the "First Reich" (the Holy Roman Empire) into a propaganda tool to create a new "Second Reich." The Hapsburgs were ancient and prestigious. If they had gone after leadership of the German nationalist community they could have beaten Prussia for it. But alas.
So France is facing Prussia, who is looking for a chance to unite Germany. Napoleon III, in the back of his little plotting mind, must have seen that Bismarck intended to use a war with France to unite Germany. But he was so confident in French arms that he thought the Prussians could be beaten. Obviously he was wrong.
Maximilian was not a good candidate for the Spanish throne. He had no sons, and I think that it would have been clear by '68 (since it was certainly clear in '63 when they adopted the Iturbides) that either him or his wife was sterile. He was a Hapsburg, in fact the brother to the current Austro-Hungarian Emperor-King, thus a party to the recent unpleasentness between Prussia and Austria.
That means that once he dies, his heir will be another Hapsburg, someone who was not raised in Spain, and though Maximilian may have been a charmingly liberal guy, proof that even the Hapsburg in their inbred retarded/conservative gene pool can produce a semi-intelligent liberal from time to time, the Spaniards own experience tells them that Maximilian's Hapsburg heir will not be in the same liberal mold.
So they might be a few good years out of the man, and it will be great. But hanging over them will be the fact that the man will die, without issue (except if his wife dies, or he divorces her, so maybe we can make her fall off of a horse sometime before '68) and his heir will be a Hapsburg. If his heir is not a Hapsburg, that means the Spanish government will have to search all over again for a new royal family, so why not find some acceptably fertile prince now, and avoid all the potential unpleasantness?