Well, I can see a tacit understanding betwene the two Empires, but what interest does either side have in an alliance? After all, Prussia wasnt really seen as threat by anybody. It clearly was a rival for Austria, yes, but it was seen by everybody as the junior great power in the German Confederation, behind Austria. The 1866 war and its result was basically a huge surprise for everybody. Thus, its easy for Napoleon to rationalise that any prestige gains of him will be at the cost of Austria, since they will likely have to happen in Italy and Germany, and OTOH Napoleon simply doesnt have anything to offer to Austria.
I, too, see a tacit understanding as the best way to go. I think it's clear that, however odd it may seem, Austria is France's best friend in terms of keeping France's power relatively stronger compared to the other European powers.
Consider the following situation: the 1848 troubles result in the Second Republic, and the inevitable Second Empire, Austria suffers badly from unrest, etc. One difference: the Prussian King accepts the "crown from the gutter". At once you have provided a common cause for Austria and France to unite against, and at the same time the power they have to struggle against is weaker than in 1866 or 1870. I doubt that a German Empire this early can hold together as easily as the North German confederation was later. Napoleon III loses his Austria-hate, and together the two powers disassemble the brief liberal German Empire, say, in the mid-1850's; ensure that Prussia-Germany has angered Russia at some point recently, or that Russia's focus remains on the Ottomans and the Balkans.
Now Prussia's power is broken, and Austria unites everybody-but-Prussia and anybody west of the Rhine in a very loose, feuding pan-German confederation, preferably confederated with all of the Hapsburg possessions; France won't have to worry about Austria nearly as much while Hanoverians are screaming across a diet-hall at Hungarians. France's booty consists of Prussia's old possessions west of the Rhine. The Germans here will cause trouble, as the French caused trouble in Alsace-Lorraine, but that's fine; better France worry about internal dissent than spend millions of francs on costly and useless adventures in Mexico or Africa.
I agree with the earlier assertion that the addition of Belgium to France would be, for the most part, a net gain for France. The issue here is Great Britain. Great Britain needs to "owe one" to France (brief Crimean War?) or be otherwise occupied (Opium War? Sepoy Rebellion?) when France annexes Belgium at some point between 1830 and 1870-ish. Conclude France's foreign policy successes by having the Emperor guarantee the Pope's power in Rome while Austria is busy elsewhere, be an encourager of Sardinia's pretensions while at the same time holding them on a relatively tight leash so as not to provoke anything with Austria, and go into Egypt with a true 50-50 so that Great Britain is
forced to work with them in
everything.
You now have a French Empire that is one of the four (or five, if Abdul's Ottoman restoration works out

) powers in Europe, has reached its "natural" boundary of the Rhine, exercises power over 50% of the Italian states, and doesn't waste unnecessary funds abroad.