Yes, it does seem incredible that a rabble of ill-fed, ill-clothed soldiers could win wars against rebellious citizens as well as most other European countries. The first reason for success was size, and the second, recklessness.
All men between the ages of 18 and 25 were forcibly conscripted for military service irrespective of capacity. Men in their 30's regularly volunteered or be called up. Soldiers' first few years in the military suffered disorganization and panic. Revolutionary hype meant officers too luxuriously might be mobbed and sent to the guillotine.
Even NCOs being too harsh might also be killed or stripped of his power. However, the absolutely massive army used to hardship, brutality and conflict could rush and intimidate more civilized armies. Then Napolean, a brilliant strategist, inspired his troops and led them to victory after victory as the eighteenth century turned into the nineteenth.