The King and the piedmontese entourage were always pro-french and France was our greatest commercial patner at the time; the only two thing who blocked an alliance were the Rome question and Nappy III overeager and usually clumsy diplomacy in Italy.
There were brief but serious talk of enter the war at the side of France...but with Rome still defended by French troops was very difficult politically.
If some agreement can be reach, troops can be sent and frankly an alliance with France is more sensible towards our irredentistic objective over Austria-Hungary...and butterfly away the disastrous policy of Crispi.
You're right when you say that the king and the Piedmontese aristocracy were pro-French. However there was a couple of other major obstacles that made the alliance proposed by Nappy politically unfeasible: the first was the inclusion in such an alliance of Austria-Hungary (which was the goal of Nappy since the early 1860s and was picked up again in earnest after the 1866 war), the second one was the Italian parliament, which had been reshuffled after the annexation of Veneto and which would have blocked any serious attempt to set up a tripartite alliance with France and Austria.
What Nappy wanted in truth was an Italian guarantee of neutrality (which was a condition precedent set up by the Austrians to enter the war on the French side): unfortunately neither Nappy was willing to concede Rome nor the Austrians were ready to entertain any territorial concession (Trento?).
And in any case the Hungarian parliament was very strongly against another war in Germany.
Frankly I do not see any benefit in terms of irredentist claims by an Italian participation (as very junior partner) in a Franco-Austrian alliance. I'm quite doubtful about economical benefits either: the great agricultural crisis of the 1870s would have come anyway, and France and Italy would not have been able to set up mutually agreeable economic terms.
IMHO the best possible ally for Italy would have been Great Britain, and in second instance Prussia. In either case, keeping out of the Franco-German war (but without giving formal reassurance to either party) was the best practical solution since at least made it possible to occupy Lazio and Rome.