That is an ASB cliche for Italian, even Mussolini never care for that, their enemy was always the Austrians, even if the french goes to war...
You are so wrong on this. Even if the Austrian irredentist claims were always regarded as definitely more important than the French ones, it was always a matter of degrees, a judgement which diplomatic, political, and military factors could make swing one way or the other, much like deeming whether Austria or France was the worse geopolitical rival for Italy, irredentist grievances aside. Otherwise would Italy would have never joined the Triple Alliance and stayed for 30 years.
Moreover, Italy had a huge grievance against France in 1867, namely French support for Papal rule in Rome (something that outshined Trento and Trieste by leagues). If Prussia and France come to blows in 1867, it means Italy can give full, overt support to Garibaldi's attempt to conquer Rome (something that would force Napoleon III to declare war on Italy anyway, even if it means fighting a two-front war), and kick the French out of Latium with Prussian support. This is a very good reason to keep the Prussian-Italian alliance active in case of an early Franco-Prussian War over Luxemburg, and if Italy can net Nice, Savoy, and Corsica too in the process, and cut France down a peg, it is certainly no loss.
With a little diplomatic maneuvering masterminded by Bismarck, France may be goaded to attack Prussia and Italy, looking the aggressor bent again on Napoleonic dominance of Western Europe in the eyes of Britain and Russia, and hance left to its fate.
the last was show us how so 'well'

rolleyes

the italians can wage war(loss the most important battle and they depend of olalala French Support to win Venetia).
Italy made a poor performance in the 1866 war entirely because an handful of commanders were quite poor, the quality of the army and navy was otherwise quite good and would have ensured a much better outcome. The 1866 outcome made the bad apples be largely rooted out, so that Italy would perform in a Franco-Prussian War much better than in 1866. Not that it would have ever achieved a strategic breakthrough in the Alps before the Prussians broke the back of the French army, the realities of the Alps front being what they were. But a second front would have made the French defeat ever swifter and more decisive than OTL, after Sedan-equivalent the Italians would have got Chambery and Grenoble, swarmed Dauphine and Provence, and besieged Lyons and Marseilles.