As long as the conscripts were reinforcement to be dispatched to multiple regiments, it was usual to have them marching under a provisional commander of whatever regiment, in "Colonne de Marche".
A major for a strength of 3-4 battalions is the appropriate grade.
This would also explain why the French did not attack, if they were only trying to join the units in Germany.
"General" may be an inflationary title in Austrian accounts : better to repel a french force under a general rather than to force a conscripts column to take a detour.