Before France jumped in, it would be a disasterious affair as Austria is cleaning Sardinia's clock and the Russian army is disorganized mess with a half empty war chest and everything in transition. Post-French Entry, it would be an unacceptable violation of the Vienna System power balance to cut more that Lombardy off Austria and all the other powers are already wary of her ambitions following Crimes,so she loses the peace since she won't be allowed to extract anything from the defeated.
There were just two weeks (27 April to 10 May) between the Austrian war declaration and the arrival of the French troops and the Austrian CiC, Gyulai, could not be accused of being a decisive general. He dithered until 7 May before moving forward, and by then it was too late.
It was in many ways a situation that will be repeated in 1870: the side which declares war is not ready to immediately move
It is interesting that on 18 March Russia had proposed a conference of the Powers in Paris, which was supported by the British and by the Prussians. Napoleon III, under the influence of his Foreign Minister, Walewski, accepted the conference even if Cavour had traveled to Paris to convince him to keep faith the the pact of Plombieres. Cavour had to accept the conference too,on 18 April, and the demobilization of the Piedmontese army (also France and Austria should demobilize their forces), subject to a participation of Piedmont-Sardinia to the Congress. Austria refused to countenance a Piedmontese participation and on 23 April delivered an ultimatum to Piedmont asking for immediate demobilization. Bad move, overall, which isolated Austria on the diplomatic side.