So a Franco-Prussian alliance isn't allowed?
Go with OTL. They're both in NATO, and allied today.
Seriously, though, a good first step is the Austro-Prussian War. Bismarck and Napoleon III discussed the war together, and Napoleon III agreed not to aid Bismarck. So if that meeting went better, France could end up pro-Prussian. Maybe not actually fighting in the war, but wit sympathies towards the Prussians.
That would be a great starting point for a Franco-Prussian alliance, and it's not too hard to imagine an alliance shortly after.
After that, have French/Prussian relations slowly get better. Prussia begins absorbing minor German statelets, but at a rate too slow for France to really care about, especially giving warming relations. When Prussia gets large enough (probably not as big as OTL, since this relies on less French fear of growing Prussian power), it renames itself Germany in a pompous ceremony. An early alliance (rather than just friendship) between the two would be best, so France isn't as worried about German unification.
An easy, cheating way is just to use the Revolutions of 1848. Prussia becomes a liberal democracy, minor German nations join in to form Germany (a major point of the German revolutions was that they wanted German unity), and the Republics of France and Germany begin the Entente.