This scenario has been rather extensively discussed and developed in this quasi-TL discussion thread of mine: the "
European War of 1870" (I hope to turn it into a full-fledged TL eventually).
To sum it up, if Austria joins France, it is pretty sure that Italy and Russia would intervene on the side of Prussia/Germany. The former because of previous Italo-Prussian alliance bonds, irredentist claims of Italy on both powers, and Austro-French hostility to Italian annexation of Rome. The latter because of standing secret accords between the Russian government and Bismarck that committed Russia to attack Austria in Galicia if Austria joined France. Britain stays neutral since they had been cleverly persuaded by Bismarck's dplomacy that this war is all the fault of Napoleon III and French expansionism in the Rhineland and the Low Countries, which they didn't fancy one bit.
Austria is attacked by three sides and swiftly collapses (all the more so since the Hungarians, that never were enthused about a dynastic Habsburg revenge war on Prussia, would see the writing on the wall and rise up as soon as the military situation turns bad).
France has to fight a two-front war and is screwed even worse than OTL, losing Nice, Corsica, Savoy, and sphere of influence rights in Tunisia to Italy on top of Alsace and Lorraine to Germany (which is also likely to buy Luxemburg from the Netherlands and annex it with part of the French reparations). It is also quite possible that Germany and Italy seize and partition French shares of the Suez Canal and French colonial holdings in Indochina.
Bismarck is forced to accept Grossdeutchsland as inevitable. The Habsburg Empire is partitioned, Austria gets Galicia and Bukovina, Germany gets Austria, Bohemia-Moravia, South Tyrol, and Slovenia, Italy gets Trentino, the Austrian Littoral, and Dalmatia, Hungary becomes independent keeping Slovakia and Transylvania, as well as Croatia which gets expanded federal autonomy. Toss a dice to decide whether Fiume is awarded to Italy, Germany, or Hungary.
Germany, Italy, and Hungary establish an exceedingly stable Triple Alliance, and quite possibly, a customs and currency union as well. France suffers a worse Commune insurrection, and after the war turns even more politically instable and revanchist against the German-Italian bloc than OTL. Some kind of autoritarian-revanchist regime change is quite likely, such as a reactionary Bourbon restoration, a Boulangist populist-militarist republican dictatorship, or quite possibly a mix of the above.
The anti-Ottoman insurrections in the Balkans and the Russo-Turkish wars happen on schedule or slightly earlier, the outcome is much like OTL because Germany and Italy mediate in the *Congress of Berlin between Britain and Russia to prevent excessive Russian aggrandizement in the Balkans, although the outcome is going to be a bit less favorable to the Ottomans than OTL since Austria is no more. I.e. Bulgaria is made autonomous and united in its modern borders, Crete is made a protectorate of the great powers, Greece gets Thessaly and southern Epirus, Italy gets a protectorate over Tunisia and Libya (and Germany one over Morocco if it cares to).
The main geopolitical issue of Europe becomes whether the German-Italian-Hungarian Triple Alliance shall ally with Russia or with Britain in the long term, although as long as Bismarck is alive (due to the immense prestige reaped with being the author of the complete national unification of Germany, it is likely that he remains in change pretty much as long as he lives), he strives to maintain a balancing act of the CPs between Russia and Britain, and to keep both reasonably content, with a fair degree of success. After him, the CP shall be forced to pick a side, and the scorned power shall ally with France.
Those alliance blocks (Germany-Italy-Hungary and either Britain & the Ottomans or Russia; France and either Russia or Britain & the Ottomans) are likely to endure all the way into WWI, if it ever happens (and if it does, the CP are all but sure to win it, short of the USA siding early with the Entente).