Best thing would be to have the Austrians not be completely defeated at Königgrätz, giving the French time to join in on the Austrian side. France and Austria manage to defeat the Prussians. Germany remains a Confederation under Austria, and perhaps France gains parts of the Rhineland. Hell this would also butterfly the Austro-Hungarian compromise, making Austria more stable.
France gaining parts of the Rhineland would already weaken the position of Austria and the other victorious states, since the same movement which contributed to the re-unification of Germany, will heavily criticize them for it. In fact that might well be the TTL German equivalent of Alsace-Lorraine...
Another issue is that France wasn't that popular in Vienna after the Austro-Sardinian war were France had supported Sardinia.
Also by this point Austria still controlled the Venetia part of the kingdom of Lombardia-Venetia. IOTL Italy joined Prussia in this conflict and also attacked Austria.
So maybe instead of direct French territorial gains, Austria much instead cede Venetia to France, who in turn transfers it to Italy. This would result in Austria basically leaving Italy, something France wanted, though they will keep more or less the same territories they kept IOTL in 1866 (most of which had been 'Austrian', Hungarian and/or Habsburg for centuries).
However without an armed conflict with Italy, Austria will be able to deploy more men against Prussia.
Also a more divided Germany will also be in the interest of France. The house of Schleswig-Holstein-Sonderburg-Augustenburg might also be able to now rule Schleswig-Holstein, which would be a member state of the German Confederation.