It seems to me that at this point command of the Italian Army was not a very desirable appointment except for general Bonaparte who already planned offensives of 1794 and 1795. The front was not considered important and the army was the most neglected one both in the terms of supplies and reinforcements. With the nominal strength of over 100,000 the real numbers were around 30,000. It’s commander, Kellerman, asked Carnot for reinforcements and ... was replaced by Scherer who soon afterwards resigned and was replaced by Bonaparte who did not get any reinforcements or supplies and launched an offensive with 37,000 troops against more than 50,000 (or 90,000?) in what was considered a good defensive position. His famous address to the troops clearly described both situation and perspectives.”.You are naked and hungry...It is my design to lead you into the most fertile plains of the world . Rich provinces and great cities will be in your power ; there you will find honor , glory , and wealth .” From the Directorate’s point of view this could look,as a reasonable appointment: (a) honor of getting an army command, (b) familiarity with the theater and (c) a minimal risk for the Republic if inexperienced army commander screws up. Probably they expected something limited in scope like Saorgio Offensive (executed by Bonaparte’s plan)
As for Eugene, he would probably enter the military service and, AFAIK, he was talented enough to make a decent career, especially if he starts as Bonaparte’s aid: even if there is no marriage to Josephine, Barras could recommend him. Of course, chances to raise as high as in OTL would be close to zero.