Entering the Austrian military service, Zach became a Major in 1788, an Oberstleutnant in 1793, and an Oberst in 1795. He served as Chief of the Quartermaster General Staff (chief of staff) to Johann Peter Beaulieu from 8 April to June 1796 during the Montenotte Campaign, the Battle of Lodi, and the Battle of Borghetto. In June he was succeeded by Franz von Lauer when Dagobert Sigmund von Wurmser replaced Beaulieu. Subsequently, he served on Paul Davidovich's staff during the Battle of Rovereto on 4 September. In 1797, Zach served on a commission to analyze the reasons for Austria's defeat. He noted that lower-ranking generals displayed little initiative because there were too many regulations. He found that regimental officers showed more interest in pay and privilege and drill than in learning how to make fighting units more efficient. He saw that officers were indifferent toward the rank and file, and that the lower ranks had little trust or enthusiasm for their leaders.